DECEMBER 2012 IEEE MTT-V060-I12 (2012-12B) [60, 12 ed.]

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DECEMBER 2012

VOLUME 60

NUMBER 12

IETMAB

PART II OF TWO PARTS SPECIAL ISSUE ON 2012 INTERNATIONAL MICROWAVE SYMPOSIUM 2012 Symposium Issue

Montreal, Canada, site of the 2012 IEEE MTT-S International Microwave Symposium

(ISSN 0018–9480)

IEEE MICROWAVE THEORY AND TECHNIQUES SOCIETY

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J-C. CHIAO M. GUPTA

S. KOUL L. PIERANTONI

D. PASQUET G. PONCHAK D. SCHREURS

R. SORRENTINO B. SZENDRENYI R. WEIGEL

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K. WU Q. XUE

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Digital Object Identifier 10.1109/TMTT.2012.2233053

DECEMBER 2012

VOLUME 60

NUMBER 12

IETMAB

(ISSN 0018-9480)

PART II OF TWO PARTS

SPECIAL ISSUE ON 2012 INTERNATIONAL MICROWAVE SYMPOSIUM

2012 Symposium Issue

Editorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. E. Ponchak

3892

MICROWAVE SYMPOSIUM PAPERS

Theory and Numerical Methods Evanescent-to-Propagating Wave Conversion in Sub-Wavelength Metal-Strip Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Md. Memarian and G. V. Eleftheriades Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. Rodríguez-Berral, C. Molero, F. Medina, and F. Mesa Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. S. Ochoa and A. C. Cangellaris Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Kabir and R. Khazaka Passive Components and Circuits CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Gupta, D. L. Sounas, H. V. Nguyen, Q. Zhang, and C. Caloz Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines . . . J. S. Sun, H. Lobato-Morales, J. H. Choi, A. Corona-Chavez, and T. Itoh

3893 3908 3919 3927

3939 3950

(Contents Continued on Page 3890)

(Contents Continued from Page 3889) Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Wu, X. Yang, S. Beguhn, J. Lou, and N. X. Sun Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. A. Ruiz-Cruz, M. M. Fahmi, and R. R. Mansour Narrowband Microwave Filters With Mixed Topology . . . . . . . . . . . . . . . . . . . . . G. Macchiarella, M. Oldoni, and S. Tamiazzo -Mode Dielectric Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Inline Pseudoelliptic Orthogonal Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Bastioli and R. V. Snyder -Band Fully Tunable Cavity Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Yassini, M. Yu, and B. Keats A

3969 3980

Electron Devices and Device Modeling Multiphysics Modeling of RF and Microwave High-Power Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. H. Aaen, J. Wood, D. Bridges, L. Zhang, E. Johnson, J. A. Plá, T. Barbieri, C. M. Snowden, J. P. Everett, and M. J. Kearney Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range . . . . . . . . . . . . . . . . . . . . . S. P. Voinigescu, E. Dacquay, V. Adinolfi, I. Sarkas, A. Balteanu, A. Tomkins, D. Celi, and P. Chevalier

4013

Hybrid and Monolithic RF Integrated Circuits Resistive Graphene FET Subharmonic Mixers: Noise and Linearity Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. A. Andersson, O. Habibpour, J. Vukusic, and J. Stake High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Roberg, T. Reveyrand, I. Ramos, E. A. Falkenstein, and Z. Popović Passive Subharmonic Generation Using Memoryless Nonlinear Circuits . . . . . . . . . . . . . . . . . . . . . Z. Safarian and H. Hashemi Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.-C. Yeh, C.-C. Chiong, S. Aloui, and H. Wang 4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Aja Abelán, M. Seelmann-Eggebert, D. Bruch, A. Leuther, H. Massler, B. Baldischweiler, M. Schlechtweg, J. D. Gallego-Puyol, I. López-Fernández, C. Diez-González, I. Malo-Gómez, E. Villa, and E. Artal A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.-H. Chen, S. R. Helmi, H. Pajouhi, Y. Sim, and S. Mohammadi PA Efficiency and Linearity Enhancement Using External Harmonic Injection . . . . . A. Dani, M. Roberg, and Z. Popović F Mode Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier Using In-Band Continuous Class-F Transferring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. Chen and D. Peroulis High-Gain and High-Efficiency EER/Polar Transmitters Using Injection-Locked Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.-T. Chen, T.-S. Horng, K.-C. Peng, and C.-J. Li A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer . . . . . . . . . . . . . . . . . A. Tang, D. Murphy, F. Hsiao, G. Virbila, Y.-H. Wang, H. Wu, Y. Kim, and M.-C. F. Chang Instrumentation and Measurement Techniques Generalization and Reduction of Line-Series-Shunt Calibration for Broadband GaAs and CMOS On-Wafer Scattering Parameter Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.-C. Huang and Y.-C. Chen Experimental Characterization of Stability Margins in Microwave Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Otegi, A. Anakabe, J. Pelaz, J.-M. Collantes, and G. Soubercaze-Pun A 1–8-GHz Miniaturized Spectroscopy System for Permittivity Detection and Mixture Characterization of Organic Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Helmy and K. Entesari Accurate Nanoliter Liquid Characterization Up to 40 GHz for Biomedical Applications: Toward Noninvasive Living Cells Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Chen, D. Dubuc, M. Poupot, J.-J. Fournié, and K. Grenier RF Applications and Systems An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Kim, A. Georgiadis, A. Collado, and M. M. Tentzeris On the Detection of Frequency-Spectra-Based Chipless RFID Using UWB Impulsed Interrogation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. Kalansuriya, N. C. Karmakar, and E. Viterbo Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Yu, L. Guan, E. Zhu, and A. Zhu

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4035 4043 4053 4066 4080 4089 4097 4107 4117 4129

4138 4145 4157 4171

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(Contents Continued from Page 3890) Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Ziegler, B. Schulte, J. Sabater, S. Bovelli, J. Kunisch, K. Maulwurf, M. Martinez-Vazquez, C. Oikonomopoulos-Zachos, S. Glisic, M. Ehrig, and E. Grass GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. A. García, R. Marante, and M. de las Nieves Ruiz Lavín

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Information for Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CALLS FOR PAPERS

Special Issue on Phased-Array Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2012 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Available online at http://ieeexplore.ieee.org

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Editorial

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HE IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) was held in Montreal, QC, Canada, on June 17–22, 2012, and the conference Chair, Prof. Ke Wu, introduced several exciting ideas to stimulate paper submissions to the conference. First, the conference committee made a determined effort to increase publicity, especially in Asia. Second, and definitely more controversial, they reduced the paper length from the traditional four pages to three pages. The thought behind this was that it would make it easier for authors to write a journal paper based on the conference paper because the conference paper would not contain as much technical information. Thus, the authors would have an easier time meeting the IEEE MTT-S threshold that every paper, whether conference or journal, must present substantially new technical material. It must be stated that Prof. Wu succeeded. There were a record number of submissions to the IEEE MTT-S IMS, and there were a record number of submissions to this TRANSACTIONS’ “Special Issue on the 2012 International Microwave Symposium.” In fact, there were too many submissions for the reviewers, the Associate Editors, and me to complete all of the papers before the deadline for the December issue. Therefore, I have divided the IEEE MTT-S IMS “Special Issue on the 2012 International Microwave Symposium” into two parts, which will be published in this TRANSACTIONS’ December 2012 and January 2013 issues. In the January 2013 Special Issue, I will write a full editorial detailing the number of papers, the acceptance rate, and my opinion on the success or failure of the three-page experiment. In the meantime, please enjoy this Special Issue with 32 papers based on papers presented at the 2012 IEEE MTT-S IMS. DR. GEORGE E. PONCHAK, Editor-in-Chief NASA Glenn Research Center Cleveland, OH 44135 USA Digital Object Identifier 10.1109/TMTT.2012.2225512

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Evanescent-to-Propagating Wave Conversion in Sub-Wavelength Metal-Strip Gratings Mohammad Memarian, Student Member, IEEE, and George V. Eleftheriades, Fellow, IEEE

Abstract—Transmitting sub-wavelength information to the far-zone is of great interest for various electromagnetics and optics applications, e.g., for overcoming the diffraction limit in imaging or enabling multiple-input/multiple-output operation in closely spaced antennas. The common phenomenon in these applications is the conversion of evanescent to propagating waves. In this paper, we rigorously analyze and study evanescent-to-propagating wave conversion based on sub-wavelength metallic strip gratings. A theory is provided, which fully captures all diffracted fields and clearly highlights this conversion phenomenon. The Green’s function of the strip gratings is constructed by introducing the spectral impulse response. This method solves the problem of the aperiodic excitation of the periodic grating and along the way provides insight and clear explanation of the evanescent-to-propagating wave conversion that takes place. All proposed results are validated against full-wave electromagnetic simulations. The theory is used to highlight and explain “extraordinary” transmission through a sub-wavelength metal strip grating when excited by a current source. Finally, an interesting application is presented where a nonradiating arrangement of sources is made to radiate by converting and diffracting its reactive near-field spectrum into the propagating regime using a simple metal strip grating. Index Terms—Electromagnetic diffraction, extraordinary transmission, gratings, Green’s function, imaging, periodic structures, spectrum conversion, sub-wavelength resolution.

I. INTRODUCTION

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HE NEAR-FIELD spectrum contains spatial information about the sub-wavelength variations of a source/object distribution. This information in the near-field is carried by evanescent waves, which decay exponentially with distance. The sub-wavelength information is therefore typically lost in the far-zone since only the propagating waves survive. For applications where small distances, compared to the operating wavelength, are of significance, such information cannot be resolved in the far field due to this limiting factor. This is the main cause of the diffraction limit. Several techniques have been reported in the literature, where sub-wavelength features of an object could be resolved in the far-zone. For example, in a far-field optical super-lens setup [1], Manuscript received June 28, 2012; revised September 18, 2012; accepted September 20, 2012. Date of publication November 16, 2012; date of current version December 13, 2012. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada M5S 2G5 (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2221734

sub-wavelength-spaced nanowires (object) were imaged in the far field, using a silver film and a diffraction grating placed near the object. In another experiment involving time reversal [2], independent multiple-input/multiple-output (MIMO) channels were realized in closely spaced antenna elements. Although the elements were spaced at sub-wavelength distances, they were individually selected from the far-zone, by placing scatterers in the form of metallic brushes in the near-field zone of the antenna array. In a related study [3], it has been demonstrated that waves emanating from sources can be refocused with sub-wavelength resolution onto an image plane using phase-conjugating screens, provided that identical scatterers are placed both near the sources and the image plane. The phenomenon, which is common among these applications, is spectrum conversion, and specifically, the conversion of evanescent-to-propagating waves. In order to retain the subwavelength resolution at the far-zone, the near-field spectrum is converted to a propagating spectrum, which can then reach the far-zone in addition to the usual propagating spectrum. This spectrum conversion is normally the result of a diffraction or scattering process in the near field, e.g., due to a grating in [1] and metallic brushes in [2]. It is the purpose of this paper to rigorously analyze and study the phenomenon of the conversion of evanescent to propagating waves by ordered periodic structures, excited by a finite aperiodic source, and to utilize it for a novel application involving an array of closely spaced current elements. Specifically, a commonly studied canonical metallic strip diffraction grating [4] is used in this study. The desired spectrum conversion is first demonstrated in its fundamental form for a single plane wave incident on such a sub-wavelength period grating. The phenomenon is then shown for a single finite source placed near the grating, and ultimately for arbitrary arrangements of sources, for both polarizations. This study is supplemented by a theory that predicts every scenario of interest, which we first introduced in [4], and is significantly expanded herein. The theory treats the “aperiodic” excitation of a “sub-wavelength periodic diffraction grating.” We depict a fully spectral view of the complex scattering scenario that takes place and makes the link to the idea of evanescent-to-propagating conversion. We achieve this through the analytical development of the Green’s function, and explicitly show the phenomenon for actual finite sources. The method is based on the plane-wave scattering by the grating and accounts for diffraction due to the complete fields emanating from the source, including the reactive near field. The solution is carried out directly in the spectral domain through the introduction of the spectral impulse response (SIR), which makes

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Fig. 1. Aperiodic single source excitation of an infinitely long periodic metal strip grating of period and gap (from [4]).

it particularly simple to monitor the evanescent-to-propagating wave conversion, and identify the far-zone field by asymptotic methods. The final expressions appear as a natural expansion of Floquet modes, which offer physical insight to the diffraction process to complement other semianalytical representations [5]–[18], rigorous [19], or fully numerical full-wave approaches such as finite-difference time-domain (FDTD), method of moments (MoM), or finite-element method (FEM) simulations. This paper is organized as follows. In Section II, we set up our aperiodic problem of interest to be solved and demonstrate conversion of a single evanescent wave to a propagating wave using a metal strip grating. In Section III, the general planewave scattering solution is described and used in Section IV to determine the SIR of the grating. In Section V, we develop the Green’s function of the grating based on the SIR, as well as the response to actual current excitations and provide far-field approximations. The theory is validated with a full-wave solver in Section VI. Evanescent-to-propagating conversion of waves emanated from a current source near the grating is demonstrated in Section VII, and in Section VIII, the idea is used to convert “invisible” antenna arrays to highly radiating ones. II. METAL STRIP GRATING AND DEMONSTRATION OF EVANESCENT-TO-PROPAGATING WAVE CONVERSION A. Simplified Problem Space In many microwave and optical applications, a periodic structure is driven by finite source(s) that are placed in its vicinity. Some examples include sources above artificial periodic surfaces [5], excitation of leaky-wave antennas [6], directive beaming in the presence of partially reflection surfaces [15], and sources near metamaterial structures [7]. To solve for the fields, the break of the periodicity due to the aperiodic excitation complicates the standard periodic analysis that uses the Floquet eigenmodes. Ideally, it would be desirable to find the aperiodic Green’s function of the periodic structure in analytical closed form, which is equivalent to determining the field solution when a single point source (space impulse) drives the periodic domain. To date, numerical and semianalytical methods have been developed for solving this class of problems [8]–[14]. Perhaps the most notable method is the array scanning method (ASM) [8], which has been combined with the MoM [9], [10] and with FDTD [12], [13]. In this study, we consider the problem space shown in Fig. 1. As shown, a canonical infinitely long diffraction grating is aligned in vacuum along the -axis in the – -plane. The grating is an array of metal strips, with period , separated by

Fig. 2. Unit cell of the metal strip grating and appropriate boundary conditions for full-wave analysis.

a distance , and the strip width is – . The strips are zero thickness perfect electric conductors (PECs). Two polarizations are possible in the 2-D domain: transverse electric (TE) with three field components , and transverse magnetic (TM) with three field components . All fields are time–harmonic phasors of . For the aperiodic analysis, a single frequency source excites the grating at an arbitrary distance , making the overall problem aperiodic. B. Spectrum Conversion in an All Periodic Grating Problem Here we show that indeed a single evanescent wave can be converted to a propagating plane wave, in the infinite periodic metal strip grating, through periodic full-wave simulation. Consider the simulation setup of a single unit cell shown in Fig. 2 for a metal strip grating with period and an incident plane wave, indicated by the propagation vector . The problem is open in the -direction. It is known that a single plane-wave incident on an infinite grating with an incident wavenumber diffracts into many higher order modes. The higher order mode wavenumbers are governed by the phase-matching condition , where is the grating wavenumber. In other words, a grating can provide shifts in the transverse wavenumber of the incident wave by integer increments of . For applications such as [1]–[3], where near-field data is to be transmitted to the far field, the grating must provide a wavenumber shift larger than . This directly implies a sub-wavelength period and is the core reason we are interested in the study of sub-wavelength gratings for the purpose of evanescent-to-propagating spectrum conversion. For example, a sub-wavelength period size of corresponds to a grating wavenumber of . With such a grating, we speculate that any waves within the spectrum range of where is an integer, would be converted to the propagating region , in the lower half-space of the problem, and waves with any other incident wavenumbers would not diffract into a propagating wave. We shine the grating with two different evanescent waves in the simulator having the form (1)

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Fig. 4. Spectral representation of transmission through a grating with . An incident wave of falls outside of any conversion band and does not convert to a propagating wave, but an incident wave of is converted to a propagating wave of via diffraction order, . and weight

Fig. 3. Evanescent wave is incident on a grating from . (a) Complex , along the -axis, in the transmission region magnitude of TE electric field, . (b) in the unit cell for the case of no of the grating unit cell . (c) constant in the unit cell for the case conversion . (d) Absolute value of real of conversion to a propagating wave, for the case of showing the excited propagating wave part of and its direction.

, and , where the second exponent is chosen such that the wave is decaying along the -direction. Fig. 3(a) shows the complex magnitude of the total field plotted along the path for the two incident cases in the transmission region . For an incident wave with , the dashed curve shows that the total field decays to zero in an exponential manner as we move away from the grating. This [as well as Fig. 3(b)] shows that there are no propagating waves in the transmission region of the grating and the transmitted field consists solely of evanescent waves. For the incident evanescent wave of , the solid curve in Fig. 3(a) [as well as Fig. 3(c)] shows that the total field magnitude is now a nonzero constant for , implying a propagating wave with no decay when moving away from the grating. Hence, an evanescent-to-propagating wave conversion is observed. Fig. 3(d) shows the absolute value of the real part of the electric field for the case of . It can be seen that the transmitted field has wavefronts corresponding to a single propagating wave. Since this wave is converted from an incident evanescent wave of , it propagates with , due to the phase matching condition.

Fig. 5. Scattering due to an incident plane wave on the grating [20] (from [4]).

A spectral view of the above two simulations is shown in Fig. 4, where only the window between and can be converted to the propagating region, due to the choice of the grating period. An incident wave at spectral location does not diffract into the propagating region. However, the wave at does diffract into the propagating region having a transmitted wave number of . The amplitude of the diffracted wave is also multiplied by a complex weight called , which will be determined later using the SIR theory. It must be noted that, in both cases, the transmitted diffracted field contains an infinite number of higher order harmonics, but are not shown in Fig. 4. Here, we show what only diffracts into the propagating region. III. PLANE-WAVE SCATTERING FROM A METAL STRIP GRATING Consider Fig. 5 where a single plane wave is incident on the grating. The incident wave, (TE) or (TM), has a transverse wavenumber , a longitudinal wavenumber , and an amplitude . This is an all periodic problem of period , where both the structure and excitation are infinitely periodic (2) (3)

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The transmitted fields through the grating can be represented in a Fourier series of space harmonics according to Floquet’s theorem for the -periodicity, and is given in [20] as

(4)

The unknown constants and in the two functions (10) and (11) are then found by applying the boundary condition of continuity of the tangential fields across the gap. We have carefully carried out the analysis in [20], and with some corrections, provide here the final result for the TM and TE constants

(5)

Each term in the series, , is the th-order diffracted space harmonic term, with its transverse wavenumber , phase matched to the incident wave. These harmonics have an associated weight , which is a function of the incident wavenumber . In [20], the formulation is set up such that the total reflected field consists of a reflected wave or when the gaps are completely closed, as well as the reflected scattering and from the infinitely long periodic gaps. The scattered fields and are found to be equal at the grating plane, with opposing directions of flow in the - and -directions

(6)

(7)

To find the weights , [20] approximates the tangential electric field, with a function using the edge condition, across the gaps in a single unit cell, at the grating plane. The TE/TM weights of the diffracted field are

(8)

(9)

In the TE case, across a unit cell at (grating), the tangential electric field on the strips will be zero, and the tangential field across the gaps would have a profile with a maxima in the gap center and vanishing at the strips. For the TM case, the tangential electric field will exhibit a singularity at the strip edge and attain a minimum at the gap center. Explicitly, the two functions describing the tangential TE and TM electric fields across the gap are

(12)

(13) where and are the zeroth- and first-order Bessel functions of the first kind. It can also be seen that the coefficients (12) and (13), and hence, the coefficients, are directly proportional to , i.e., the amplitude of the incident wave. Therefore, scaling the input with an amplitude scales all output terms in (4) and (5) by the same factor . In the analysis of [20], the incident wave is a propagating wave with wavenumbers and ; hence, and is real; but in fact, this solution can be extended for incident evanescent waves, where an evanescent slow wave with a lateral wavenumber is incident on the grating, and consequently, is imaginary. This extension of the solution to include incident evanescent waves is an important generalization of the plane-wave solution, which is necessary to solve for our aperiodic problem of interest. It must be noted that for evanescent waves with a high lateral wavenumber, higher accuracy modal functions (10) and (11) may be needed to account for more rapid variations of the fields across the gap. IV. SIR

METAL STRIP GRATING BASED PLANE-WAVE SOLUTION

OF

ON

We now utilize the discussed solution of scattering due to a single plane wave incident on the grating. The idea is to apply this solution to all constituent plane waves in the source field spectrum. The total transmitted field is then found by summing the contribution of scattering due to all incident waves. This is valid by virtue of the superposition principle. We shall carry out the above analysis in the spectral domain. in our spatial domain, the For any complex function is determined using the Fourier transform spectrum (F.T.) in Cartesian coordinates to be

(10) (11)

(14)

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, and is the spectral space frequency variable in the -direction. Let us now convert the previous plane-wave solution into the (2) and (3) for spectral domain. Applying F.T. (14) to , the spectrum of a single incident plane wave on the grating is

(15) which is simply a shifted impulse in the spectral domain ( domain). The spectrum of the transmitted field directly below the grating is the F.T. of (4) and (5) at given by

(16)

(17) which is an infinite sum of shifted impulses of order in the domain weighted by . Consider now the grating as a or “system” with the incident wave spectrum in (15) as the “input” spectrum to this system, and the transmitted wave spectrum (16) or (17) as the “output” from the system. The input is a spectral unit impulse (a plane wave in real space). For any shifted version of this unit impulse, the functions (16) and (17) describe the system’s output. This statement suggests that, in the spectral domain, these functions describe the “general impulse response” for the grating system, i.e., they describe the response of the system due to any shifted . Hence, we name (16) and (17) as spectral impulse the shift variant SIR of the grating, for the TE and TM polarizations respectively. The input/output relations for two functions characterizing the grating system behavior, i.e., the SIR and Green’s function, are depicted in Fig. 6(a) and (b), respectively. These functions characterize the same system, but with two different inputs. The SIR describes the response of the system when it is driven with a “spectral impulse,” at an arbitrary spectral position . In the space domain, the SIR is the plane-wave solution, i.e., the response due to a spatial exponential input. On the other hand, the Green’s function describes the response of the system due to a spatial impulse’ positioned at an arbitrary location . In the spectral domain, the spectral Green’s function describes the response of the system to a spectral exponential input, where the

Fig. 6. Grating as a system and two functions describing its behavior. (a) Spatial and spectral input/output of the SIR function representation. (b) Spatial and spectral input/output of the Green’s function representation.

effect of is now in the phase of the exponential. There is a close connection between the two functions, and as we shall see, the Green’s function for the transmitted field can be recovered from the SIR/plane-wave solution. The SIR of (16) and (17) are general impulse response funcvariant. This is particularly useful tions, and the response is as it describes the output spectrum of a grating for every arbitrary shifted version of the input impulse. As the input impulse space, the output is not a mere shift by the is shifted in the same amount in the space, but rather a unique set of factors weight the output components, depending on the input . For every impulse in the space, there exists a unique response defined by (16) and (17) that specifies what the output will be. Once the SIR is determined, we can then find the transmitted spectrum or “output” of the grating due to the field of any source, be it an aperiodic or a periodic excitation impinging on the grating, directly in the spectral domain. This is simply achieved by a superposition integral on the spectrum of the field due to these source(s), and the shift-variant SIRs (16) or (17), in the spectral domain. Since we can decompose the input spectrum into spectral impulses, which is always possible due to the F.T., we can always determine the scattered spectrum. We shall see that the far-zone characteristics of the structure for an aperiodic excitation are then derived from the asymptotic approximation of the spectrum in the far-zone. The total transmitted field due to an arbitrary input spectrum in to this system will contain scattered waves due to every the incident spectrum, and these scattered waves are governed by the shift-variant SIR. Consider an arbitrary TE field spectrum , which is a function of . This input to the grating, function can be rewritten as an integral of weighted impulses (18) The term in the integrand now is a shifted spectral impulse multiplied by . (16) describes the output due to such a shifted impulse, and is also directly proportional to the input amplitude as found in the plane-wave

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solution. Therefore, the total output of the system can be written as (19)

where stands for the spectral-domain representation of the Green’s function for TE or TM polarizations. To find the actual Green’s function in space, an inverse F.T. is required to be applied to (23) giving

which is the superposition of scattered waves due to all incident wavenumbers in . Rearranging and switching the order of integration and summation yields

(24) Incidentally, if this source is at the origin , and

(25)

(20) By means of the sifting theorem, the transmitted spectrum is

, then

and therefore,

(21) This is the transmitted or output spectrum of the grating due to an arbitrary input spectrum . This demonstrates that the output is an infinite summation of weighted copies of the input spectrum. In fact, (21) provides a clear spectral view of the diffraction process of any field distribution impinging on the grating. It is an important result, which clearly explains the relation between the input and output spectrum of the grating, and as we shall see, it will help us identify what portions of the original evanescent spectrum, and with what weights, will convert into the propagating region. The SIR approach may be utilized to solve the field for the aperiodic excitation of a periodic structure based on a general plane-wave solution.

(26) By a change of variables, we obtain (27)

In this section, the SIR approach is used to find the aperiodic response of the periodic grating in various scenarios.

which is equivalent to integrating the original plane-wave solution [(4) or (5)] over the entire spectrum of the transverse wavenumbers. This is an intuitive result, as one would expect that a single impulse source at the origin would excite all plane waves in the spectrum with equal amplitudes, and it confirms that the original plane-wave scattering solution (4) and (5) can be linked to the aperiodic excitation problem through the planewave expansion.

A. Aperiodic Green’s Function of the Strip Grating

B. Response to a Current Source Excitation

V. APERIODIC EXCITATION OF A PERIODIC DIFFRACTION GRATING

or (for TM) is the If the input spectrum spectrum due to a point source excitation, we essentially determine the aperiodic Green’s function of the structure in the spectral domain, i.e., . In our domain of interest, a possible input spectrum to the grating system, due to a point source placed at , i.e., , is (22) Using (22) in (21), we have

(23)

In (21), or can be the spectrum of the field impinging on the grating, due to one or many periodic or aperiodic sources, placed at arbitrary locations from the grating, and of any type (e.g., current or voltage source). As long as we know the total spectrum of the waves incident on the grating due to the sources, we can find the total transmitted spectrum via (21). For instance, by the plane-wave expansion of fields [21], here we find the spectrum of current sources adjacent to the grating, for TE and TM field polarizations, and use the SIR to determine the scattered spectrum. For the TE case, consider an out-of-plane line current placed at above the grating , as depicted in Fig. 7(a). By plane-wave decomposition and applying the F.T. (2), the input spectrum due to this source at is [21] (28)

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far-zone. By knowing the spectrum of the transmitted field, the Green’s function can be asymptotically approximated, and no inverse F.T. is required. The far-zone field and radiation characteristics can be obtained through the method of stationary phase: The far-field at coordinates is related to the spectrum (F.T. of tangential field at ) by asymptotic approximation, and letting , where is the far angle measured from the -axis. In a 2-D space, we have [22]

(32)

Fig. 7. Current source near grating. (a) Line source gives rise to TE polarizaattains a maximum at the gap center and reduces tion. The electric field to zero at the metal strips, as it is parallel to the neighboring metal strip boundaries. (b) -directed line dipole gives rise to TM polarization. The electric field across the gaps are normal to the metal strip boundary condition.

Therefore, we can directly write the TE and TM far-zone electric and magnetic fields for the current source excitations by applying (32) to (29) and (31),

Using (28) in (21), we find that the transmitted spectrum directly below the grating at is (33)

(29) An -directed electric line dipole [21], , on the other hand, gives rise to TM fields, as shown in Fig. 7(b). If such distribution is placed at above the grating at , the incident spectrum onto the grating would be (30) By substituting (30) into the TM equivalent of (21), the transmitted TM spectrum due to the -directed current element, directly below the grating at , is

(31) Equations (29) and (31), respectively, describe the TE and TM transmitted field spectrum due to a corresponding electric line source and electric line dipole located at . C. Far-Field The antenna characteristics of actual sources, such as the discussed current sources, placed in the vicinity of the grating, are of particular interest especially in applications such as [1] and [2]. This requires the knowledge of the field behavior in the

(34) The need to find the output spectrum due to an arbitrary excitation, and arriving at (21), can now be better understood. Not only does (21) give us a clear spectral view of the diffraction/ conversion process, it can be readily used to find the far-field, which is of interest in this study, and in general, where evanescent-to-propagating wave conversion is of interest. D. Reflected Field In the reflection region, , the field solution will have additional terms. The reflected field for a single plane-wave incidence was shown in Section III. The additional terms for the reflection region include the effect of the incident source waves and their reflection wave if the gaps were closed. It was also found from the plane-wave analysis that , i.e., the scattered field due to the infinitely periodic gap openings, is equal on the two sides of the grating, and with opposite directions of flow in the - and -directions. Therefore, for any point , we have to add the solution of a source near the infinite PEC plate solution. For the far-zone, this part of the solution can also be approximated to yield simpler expressions and this can be done directly in the space domain. Alternatively, and to be consistent with our spectral representation, the reflected spectrum can be found. For instance, for the

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line current giving rise to the TE field, the spectrum of the reflected waves that exist in above the source is

(35) where is defined in (29), and is essentially the spectrum of the scattering due to infinitely periodic gap fields, the second term is the spectrum of the -directed waves from the source translated to the plane (i.e., multiplied by ), and the third term is the reflection of the input spectrum (28) if the gaps were closed. VI. VALIDATION OF THE FIELD SOLUTION The transmitted field found using the SIR method is validated by comparing against Comsol’s 2-D full-wave simulator, at three field zones ( , near field, and far-zone). Fig. 8 shows results for a very dense grating with dimensions ( cm) and . For the plots of (a) and (b) , the source is placed in the – -plane at a very close distance of and runs infinitely along the -axis. Such an arrangement is compatible with applications [2] and [3]. The field is found using inverse F.T. on the spectrum (29) and (31). We observe close agreement between theory and simulation for both the magnitude and phase of the complex field. Fig. 8(c) shows the far-zone field due to a current source placed at away from the same dense grating. Such a scenario is usually approximated as a solid infinite ground plane with no transmission for the TE polarization, in which case image theory applies. Although this is largely valid given that the transmitted field in is small compared to the field in , some field will always leak through the gaps into the transmission region . Fig. 8 shows that the SIR method can correctly predict both the extremely weak transmitted TE far-field Fig. 8(c) (left), as well as the strong transmitted TM field Fig. 8(c) (right), leaking through the grating. It should be noted that the corresponding full-wave simulations used a large domain with over 100 grating periods terminated into absorbing walls to mimic a grating with infinite extent. This, along with the need for a very fine mesh to capture the details of diffraction, requires a long CPU time to achieve reasonable accuracy. It can be seen in the TE case that the image theory does not hold entirely, although the grating gaps are very small compared to the wavelength. The image theory approximation is mostly valid for normally incident propagating waves on the grating, as they reflect almost completely off of the sub-wavelength grating. The high grazing propagating waves, as well as the evanescent portion of the spectrum, do not bounce off the mesh reflector in the same manner. Rather, they seep through the grating as their lateral wavenumber is in the order of the grating wavenumber. For the case of the -directed line dipole excitation giving rise to TM fields, it is also seen that the overall pattern is equal

Fig. 8. Verification of TE complex field values at: (a) the grating location and (b) a near-field plane of . (c) TE/TM far-field (decibel magand the TM fields are nitude). The TE fields are excited with a line current placed at (from [4]). excited with a line dipole

on either side of the grating, as shown in Fig. 8(c) (right), and the transmission occurs with little reflection. VII. EVANESCENT-TO-PROPAGATING WAVE CONVERSION USING SIR THEORY We are now in the position to use the developed SIR theory to investigate evanescent-to-propagating conversion in finite sources such as a single current source excitation, as well as extended source excitations. A. Single Current Source Excitation To study the effect of spectrum conversion in a single source excitation setting, we find the radiation of the current sources discussed, placed both near and far from a grating of . Fig. 9(a) shows the TM incident spectrum on the grating, where a line dipole excites the domain, for two source-grating separation distances of (black curve), and [dashed red curve (in online version)]. In the case of , it can be seen that the evanescent region of the incident

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weight of each diffraction order that is multiplied by the corresponding portion of the input spectrum is shown in Fig. 9(b), i.e., the coefficients in the TM equivalent of (21). These weights are dependent on the grating geometry and are independent of the source location. Fig. 9(c) shows the radiated field in the far-zone for the two source distances of interest. In addition, Fig. 9(c) shows the radiation field for cases where the grating gaps are completely closed, i.e., an infinite PEC ground plate, for the same source distances. Similarly in the TE case, a line current is placed at these two distances from the grating, and the incident spectrum is shown in Fig. 10(a). The corresponding diffraction weights are shown in Fig. 10(b). The far-zone radiation patterns are shown in Fig. 10(c), and compared to the case of free space. B. Enhanced Transmission Through a Sub-Wavelength Grating

Fig. 9. -directed line dipole source in the vicinity of the grating for TM polarization. (a) Incident spectrum at the grating plane for a source at two distances and . (b) th-order diffraction weights ( ’s) of . (c) Far-field for spectrum conversion into the propagating region for radiation pattern (linear scale) showing exceeding transmission compared to free space and solid PEC, as predicted by SIR (solid curves) and validated with Comsol [dashed curves of corresponding color (in online version)]. Inset shows the grating and source relating to the transmission and reflection regions, .

spectrum extends well beyond the propagation region and several parts of the spectrum fall within the conversion bands of the grating. However, if the source is then taken back at a distance of , the incident spectrum is such that most of the evanescent region has decayed to zero and almost no significant portion of the spectrum falls even in the first diffraction order. The

Let us inspect the transmission region of Fig. 9(c), when the grating is close and far from the source. Intuitively we expect that when a grating is in front of the source, the transmitted field through the grating would be weaker than the free-space case, as one would think of the grating as a blockage against radiation into the transmission region. In fact, it seems logical to expect that the field magnitude in the transmission region of the grating to be somewhere between the free-space case and the case of a solid plate, which is 0. In Fig. 9(c), we can see that indeed the magnitude of the far-field for the case of [red curve (in online version)] is overall weaker than the free-space case [blue curve (in online version)], as expected; therefore, the grating is indeed acting as a blockage against transmitted radiation. However, an interesting observation can be made here, which is, in some respect, counter intuitive. For the source-grating distance of (black curve), we see that the transmitted far-field magnitude is actually stronger than the free-space case [blue curve (in online version)] at every angle in the transmission region. This counter-intuitive result shows an enhanced transmission beyond the free-space transmission for the case of a source close to the sub-wavelength grating. In other words, not only does the grating not act as a blockage for the transmitted fields, but in fact, it enhances them at the far zone. The explanation for this result is as follows. The intuitive expectation is actually only valid for propagating waves and when no significant spectrum conversion occurs. This is the case for , where most of the waves reaching the grating are propagating, as shown in Fig. 9(a) via the red curve (in online version). Therefore, what transfers to the transmission region is weaker than the free-space case radiation since the coefficient for the zeroth order is always less than unity, as shown in Fig. 9(b). However, for the case of , aside from the original propagating waves, evanescent waves have diffracted and added to the propagating spectrum, and hence, the overall radiation field is stronger than the free-space case. This is reminiscent of “extraordinary” transmission [23] through a subwavelength grating enabled by the evanescent-to-propagating wave conversion properties of the grating. It must be noted that, for the TE case of Fig. 10(c), we do not observe an extraordinary transmission beyond the free-space transmission. This is primarily due to the weakening effect of

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TABLE I TOTAL RADIATED POWER FROM SINGLE SOURCE AT 1 GHz

C. Radiated Power The radiation patterns of Fig. 9(c) also show a stronger overall magnitude, in both the reflection and transmission regions, for the case of an electric line dipole placed at a distance of from the grating. This leads us to examine the total radiated power more closely for the line sources at an arbitrary chosen frequency of 1 GHz. The total radiated power by a source arrangement, per unit length in the -direction, calculated using the far-zone electric or magnetic fields integrated over an enclosing cylindrical surface of radius around the antenna arrangement is

(36) As a benchmark, the total radiated power in the free-space per unit length in the -direction, for the electric line dipole of strength [A m/m], can be found analytically by integration of the far-field [21] W/m

(37)

Similarly in the TE case, the radiated power per unit length in the -direction, for the electric line current [A] radiating in free space is found analytically by integrating the far electric field Fig. 10. -directed line source in the vicinity of the grating for TE polarization. (a) Incident spectrum at the grating plane for a source at two distances of and . (b) th-order diffraction weights ( ’s) for spectrum . (c) TE far-field radiation conversion into the propagating region for pattern (linear scale), with almost zero transmission. Inset shows the grating and source relating to the transmission and reflection regions, .

the grating for this polarization. In other words, the fact that the electric field cannot be tangential to the metal boundary allows for very weak fields to develop across the gaps, yielding significantly smaller coefficients , as seen in Fig. 10(b). Additionally, the denominator in the spectrum (28) weakens the incident field at higher spatial frequencies, which can also be seen in Fig. 10(a).

W/m

(38)

The total radiated power, for all other cases of interest in Figs. 9 and 10, where a source is placed near a grating at different distances, as well as close to an infinite PEC ground plane, are found by numerically evaluating (36) with the far-field data, and are tabulated in Table I. As one would expect, when the line source (TE) or line dipole (TM) is very near the PEC ground plane at , it almost does not radiate at all, i.e., the current source is shorted out because it is parallel to the ground plane in both polarizations, but again, an interesting observation from the grating results shows that the line dipole source (for TM pol.) radiates very strongly when a grating is instead placed at the same close

MEMARIAN AND ELEFTHERIADES: EVANESCENT-TO-PROPAGATING WAVE CONVERSION

Fig. 11. Arbitrary aperiodic source excitation that extends beyond a unit cell of the periodic grating. Typically the unit cells of 1–3 are solved separately, each with the corresponding portion of the total current. However, the SIR solution directly yields the total output spectrum by finding the free-space input spectrum.

distance. This total radiated power, for the combination of reflection and transmission regions is more than that of the total radiated power when the source lies in free space or if a solid infinite PEC plane is used. This is in agreement with our previous observation and confirms that indeed a higher amount of power is radiated in the far-zone altogether. This is suggestive once more that some reactive near-field around the antenna has diffracted and converted into real radiated power. D. Response to Arbitrary Source Arrangements In the most general case, we are interested in finding the response to an arbitrary source excitation, and to see if spectrum conversion can be utilized and exemplified in more involved source arrangements. Suppose that the excitation of the problem is an arbitrary arrangement of sources shown in Fig. 11. Such sources may fit entirely into a unit cell, may extend beyond a unit cell, or fall on the boundary. In the proposed SIR method, irrespective of how the source arrangement is situated with respect to the grating, and the grating periodicity, the output spectrum of the diffracted fields is determined by means of (21) as long as the spectrum of the entire source arrangement is found at the grating plane (through plane-wave decomposition or other means), and used as the input spectrum to the grating system. This is an important benefit of the SIR method compared to numerical and even semianalytical techniques such as the ASM [8]. Such scenarios of extended source arrangements may be solved using other techniques [8]–[13] by breaking up the problem into subproblems, each having different portions of the extended source arrangement, solving each subproblem individually, and then combining the results. This is a more laborious solution and requires solving multiple aperiodic problems, whereas the SIR technique yields the total diffracted field instantly. Moreover, in the SIR formulation, the excitation is decoupled from the problem solution and can be dealt with independently of the geometry of the grating. In other words, given a fixed grating, the response to any source may be found through (21) without having to resolve the grating itself. When reiterating the design to find the optimum excitation, say, for a desired far-zone behavior, the same diffraction weights can be used for different arrangements of source distribution without having to solve the full problem every time, which is in contrast to other techniques. The spectrum at a distance from the source has an exponential decay profile as seen in Figs. 9(a) or 10(a). This ensures

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Fig. 12. (a) Array of five -directed current elements, closely spaced with separation “ ” is designed to radiate weak TM fields in free space. (b) Same array placed close to a grating at distance .

rapid convergence of (21) as the higher spectral components exhibit more decay. Knowing the spectral bandwidth of the incident spectrum, one can decide where to truncate the series. As for numerical efficiency of the SIR method, an analysis such as [25] is required to investigate its performance compared to other techniques such as the ASM. For the purpose of demonstrating and characterizing evanescent-to-propagating conversion in the case of extended sources, we could prepare an incident spectrum that has a weak propagating-wave component. We can achieve this by using a source arrangement that contains very strong evanescent wave components compared to a low propagating region. In this case, the evanescent waves would diffract by the grating, and by examining the far-field, we could determine the contribution of all evanescent waves that were converted to propagating ones, as the original spectrum contained no propagating waves to begin with. After placing the grating in close proximity to the sources, the scattered fields in the transmitted region will be composed of the various diffraction orders, which are different copies of the portions of the incident spectrum, multiplied by appropriate weights. Incidentally, this investigation leads to a very interesting and novel application involving antenna arrays. Specifically, it implies the concept of converting invisible antenna arrays to highly radiating ones, as will be described in Section VIII. VIII. CONVERTING AN INVISIBLE ARRAY A HIGHLY RADIATING ONE

TO

Consider an array of five closely spaced TM line dipole sources, as shown in Fig. 12(a). This array is properly weighted through optimization to have the free-space spectrum shown in Fig. 13. As shown, there are significant lobes in the evanescent region, and the propagating region is significantly small. Such a spectrum implies that when this antenna array is in free space, it radiates very weak electromagnetic fields into the far-zone due to the weak propagating spectrum. The large lobes in the evanescent region also imply that the array is highly reactive, meaning significant reactive power is stored in the vicinity of the antenna arrangement, and a low amount of real power is radiated. Incidentally, such large lobes in the evanescent region are also encountered in super-directive arrays [24], where considerable reactive power is stored in the vicinity of the antenna array and is detrimental to their operation.

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Fig. 13. Spectrum of a five element reactive array in free space, along the array in Fig. 12(a). The spectrum shows a very weak axis, corresponding to propagating region compared to the significant lobes in the evanescent region. Also indicated are the propagating region [between dashed green lines (in online version)], and the higher order evanescent regions [between dashed red lines (in online version)] based on the grating period. (A m/m).

Consider now that a grating is placed in the close vicinity of this reactive array at a distance , as depicted in Fig. 12(b). The grating is aligned along the -axis and the array is at . We investigate the radiation characteristics of this arrangement using the SIR technique and also monitor the spectrum conversion process. It should be noted that this arrangement of five -directed current elements extends beyond the center unit cell of the grating, and each element is potentially at a different location within their respective unit cell, as the separation of the source elements is different than the grating period . To calculate the output scattered field in the transmission region, we again utilize the results of the SIR method in (31). For the incident spectrum on the grating, instead of (30), we now need the F.T. of the array’s field in free space a distance away, which is a superposition of the spectrum due to each shifted current dipoles, and explicitly it is (39) The magnitude of this input spectrum, for a grating-array distance of is shown in Fig. 14(a). This spectrum is essentially the result of the free-space propagation/attenuation of the field of the array in Fig. 12(a). In the spectrum of (39), the term creates a phase variation for propagating waves, whereas it provides a decay factor for evanescent waves as the exponent is real and negative. Moreover, evanescent waves that are at a higher spatial frequency have a larger , and would therefore experience a greater decay than evanescent waves with lower . Therefore, as we see in Fig. 14(a), the spectrum only contains two major lobes in the evanescent region, whereas the original spectrum along the array axis had repeated lobes over the spectrum, as depicted in Fig. 13. These other higher frequency lobes that were present in Fig. 13 have now decayed greatly. On the other hand, the distance is still small enough such that the two major lobes experienced little decay, and hence, the propagating region is still much weaker than these two remaining evanescent lobes. We choose the grating dimension as , i.e., a grating wavenumber of . With this dimension, the

Fig. 14. (a) Spectrum at distance away from the array in free space, in Fig. 12(b) used corresponding to the incident spectrum at for SIR. (b) th-order diffraction weights ( ’s) for spectrum con. (c) Contributions of version into the propagating region for th-order diffraction into the output propagating region. (d) Overall compared final output spectrum directly through the grating at from Comsol. with the spectrum of fields sampled at . (A m/m).

regions of evanescent waves that diffract into the propagating region are between and is a nonzero integer. The first few regions are indicated in Fig. 14(a) by dashed red lines (in online version) and the propagating region is indicated with a dashed green line (in online version).

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A. Diffraction Orders Fig. 14(b) shows the magnitude of the conversion weights for the first few diffraction orders . As we are primarily interested in what diffracts into the propagating region, the figures are showing the weights over the range . It can be seen that the weights of are mainly on the order of unity throughout the propagating region. This is in accordance with the earlier result and our expectation of diffraction of TM fields through the grating. For this polarization, the field seeps through the grating with little attenuation. Fig. 14(c) shows the magnitude of the contribution to the output propagating spectrum due to each diffraction order, i.e., the th-order term in the summation (21). These distributions are again shown for . They are the coefficients multiplied with the corresponding parts of the incident spectrum between in Fig. 14(a) and end up in the propagating region. The magnitude of the different contributions indicate that the diffraction orders are the most prominent, whereas the and diffracted orders will make little contribution. The point to be made here is that the small contributions of orders are not due to the grating attenuation, as the corresponding are all on the same order. Rather, it is due to the weak incident spectrum. For , we designed the input propagating spectrum to be weak, and for , the attenuation of evanescent waves at higher spatial frequencies significantly weakens the corresponding portion of the input spectrum. Fig. 14(d) shows the final output spectrum, i.e., the spectrum of the transmitted field directly below the grating at . This plot is the result of adding the diffraction orders . For validation, the same arrangement of sources and grating as in Fig. 12(b) is simulated in Comsol 2-D and the results are compared in Fig. 14(d). It can be seen that the calculated transmitted spectrum is in close agreement with the simulation results. B. Antenna Characteristics Fig. 15 shows the far-field pattern of the radiated magnetic field. The radiation pattern of the array without the grating is shown via a blue dashed curve (in online version). The black and dashed red (in online version) curves both show the radiation pattern for the array in the presence of the grating from SIR theory and Comsol simulations, respectively. We can see that, in the latter cases, the far-zone magnetic field attains a much larger absolute value. For example, at broadside , the farzone magnetic field is orders of magnitude stronger when the grating is present compared to the case where the array radiates in free space. This seemingly simple arrangement can have interesting implications. In essence, we start with a nonradiating and highly reactive array of sources. Once the array is placed in the vicinity of the grating, the reactive field around the source diffracts by the grating. This reactive field is gathered in the evanescent portion of the spectrum, and this diffraction causes these evanescent waves to shift in their transverse wavenumber and become propagating waves. Since the evanescent spectrum was strong,

Fig. 15. (a) Far-field radiation pattern (decibel magnitude of ) of antenna array placed near the grating calculated using the SIR method and validated with Comsol simulations. The pattern is much stronger than the pattern of the array in free space with no grating, and total radiated power is 42 dB higher. (b) Phase field in the presence of the grating predicted by the SIR method of radiated and validated with Comsol simulation.

a significant amount of energy is now released into the radiation region. This example offers a dramatic way for demonstrating the spectrum conversion process in actual sources. In this scenario, what causes the overall change in the far-field pattern is the strong contribution of the first diffracted order evanescent fields. The grating itself does little in terms of attenuating the shape of the diffracted distribution over , as the coefficient distribution is found to be in the order of unity over this range. Nevertheless the key functionality of the grating is exploited here, which is adding up various portions of the input spectrum into the propagating region. From the SIR formulation of the far-field, we are directly identifying the radiating modes. For , the zeroth-order mode in the summation is the direct conversion from the incident propagating spectrum, with the conversion factor . The other terms in the summation represent radiating modes, which are a result of conversion from evanescent modes in the incident spectrum to propagating modes with conversion factor ( nonzero). For the invisible array in free space of Fig. 12(a), the total power per unit length radiated by the system is 0.0651 W/m, but when the same antenna arrangement is placed near the grating as in Fig. 12(b), numerical evaluation of the power from the far-

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field data of Fig. 15 yields a radiated power of 1000 W/m. This value is a factor of 15 000 larger than the total power radiated in free space, equivalent to a 42 dB increase in radiation power. This simple concept of converting nonradiating sources to radiating ones by near-field scattering, as demonstrated here using a grating, can have various novel applications including detection and sensing. For instance, the weak field due to the original array in free space may be undetectable or “invisible” to a far-field observer in the presence of an ambient electromagnetic field/noise, depending on their relative strengths. By placing the grating in front of the source arrangement, a much stronger field reaches the observation point in the far-field, which may be designed to be higher than the noise floor, and hence, the presence of the array is sensed or detected in the observation location. IX. CONCLUSION The SIR technique is introduced and used to find the field response to the aperiodic excitation of a periodic metal strip grating and specifically for the purposes of illustrating evanescent-to-propagating wave conversion. In this method, the plane-wave solution is converted to the spectral domain to determine the grating SIR. The spectrum of the fields of an arbitrary source in free space is also found separately, and the total response is calculated through a superposition integral. The SIR method is formulated to clearly show and theorize the spectrum conversion capabilities of metal strip gratings, and identify contributions of the various diffraction orders. The results are validated against full-wave simulations with a commercial field solver and show that the SIR method can correctly predict the diffraction process in all cases of interest, and is only limited by the accuracy of the underlying plane-wave solution. The evanescent-to-propagating wave conversion in the strip grating is shown to increase the transmission field through a sub-wavelength grating at least for the TM polarization compared to free-space propagation, as well as the overall radiated power. This shows that the grating does not necessarily act as a blockage for the transmitted field. In fact, the grating can enhance the transmission beyond the free-space transmission, which is reminiscent of the “extraordinary transmission” through a sub-wavelength periodic structure. We have also demonstrated how an “invisible” array can be made “visible” to a far-field observer by significantly increasing its radiation pattern strength and power. This can be thought of as some kind of giant “extraordinary transmission” enabled by a sub-wavelength grating and can find applications in detection and sensing. REFERENCES [1] Z. Liu et al., “Far-field optical super lens,” Nano Lett., vol. 7, no. 2, pp. 403–408, Jan. 2007. [2] G. Lerosey, J. Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 23, vol. 315, no. 5815, pp. 1120–1122, Feb. 2007. [3] O. Malyuskin and V. Fusco, “Far field subwavelength source resolution using phase conjugating lens assisted with evanescent-to-propagating spectrum conversion,” IEEE Trans. Antennas Propag., vol. 58, no. 2, pp. 459–468, Feb. 2010.

[4] M. Memarian and G. V. Eleftheriades, “Spectral-impulse-response approach for analyzing the aperiodic excitation of a periodic diffraction grating,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [5] H.-Y. D. Yang, “Theory of microstrip lines on artificial periodic substrates,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 5, pp. 629–635, May 1999. [6] T. Zhao et al., “2-D periodic leaky-wave antennas—Part I: Metal patch design,” IEEE Trans. Antennas Propag., vol. 53, no. 11, pp. 3505–3514, Nov. 2005. [7] A. Grbic and G. V. Eleftheriades, “Negative refraction, growing evanescent waves, and sub-diffraction imaging in loaded transmission-line metamaterials,” IEEE Trans. Microw Theory Techn., vol. 51, no. 12, pp. 2297–2305, Dec. 2003. [8] B. A. Munk and G. A. Burrell, “Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy halfspace,” IEEE Trans. Antennas Propag., vol. 27, no. 5, pp. 331–343, May 1979. [9] H.-Y. D. Yang, “An analytical array scanning method for field computations of sources within a periodic structure,” in IEEE Antennas Propag. Soc. Int. Symp., Aug. 1999, vol. 4, pp. 2204–2207. [10] H.-Y. D. Yang and D. R. Jackson, “Theory of line-source radiation from a metal-strip grating dielectric-slab structure,” IEEE Trans. Antennas Propag., vol. 48, no. 4, pp. 556–564, Apr. 2000. [11] F. Capolino, D. R. Jackson, and D. R. Wilton, “Fundamental properties of the field at the interface between air and a periodic artificial material excited by a line source,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 91–99, Jan. 2005. [12] R. Qiang, J. Chen, F. Capolino, D. R. Jackson, and D. R. Wilton, “ASM-FDTD: A technique for calculating the field of a finite Source in the presence of an infinite periodic artificial material,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 4, pp. 271–273, Apr. 2007. [13] D. Li and C. D. Sarris, “Efficient finite-difference time-domain modeling of driven periodic structures and related microwave circuit applications,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 8, pp. 1928–1937, Aug. 2008. [14] R. Sigelmann and A. Ishimaru, “Radiation from periodic structures excited by an aperiodic source,” IEEE Trans. Antennas Propag., vol. AP-13, no. 3, pp. 354–364, May 1965. [15] D. R. Jackson, P. Burghignoli, G. Lovat, F. Capolino, J. Chen, D. R. Wilton, and A. A. Oliner, “The fundamental physics of directive beaming at microwave and optical frequencies and the role of leaky waves,” Proc. IEEE, vol. 99, no. 10, pp. 1780–1805, Oct. 2011. [16] G. Lovat, R. Araneo, and S. Celozzi, “Dipole excitation of periodic metallic structures,” IEEE Trans. Antennas Propag., vol. 59, no. 6, pp. 2178–2187, Jun. 2011. [17] S. Paulotto, G. Lovat, P. Baccarelli, and P. Burghignoli, “Green’s function calculation for a line source exciting a 2-D periodic printed structure,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 4, pp. 181–183, Apr. 2010. [18] S. Paulotto, P. Baccarelli, P. Burghignoli, G. Lovat, G. W. Hanson, and A. B. Yakovlev, “Homogenized Green’s functions for an aperiodic line Source over planar densely periodic artificial impedance surfaces,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 7, pp. 1807–1817, Jul. 2010. [19] M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Amer., vol. 71, pp. 811–818, Jul. 1981. [20] A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering. Englewood Cliffs, NJ: Prentice-Hall, 1990. [21] P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields. New York: Pergamon, 1966. [22] E. V. Jull, Aperture Antennas and Diffraction Theory. Stevenage, U.K.: IET, 1981. [23] T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature, vol. 391, pp. 667–669, Feb. 1998. [24] S. A. Schelkunoff, “A mathematical theory of linear arrays,” Bell Syst. Tech. J., vol. 22, no. 1, pp. 80–107, 1943. [25] F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propag., vol. 55, no. 6, pp. 1644–1655, Jun. 2007.

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Mohammad Memarian (S’08) received the B.A.Sc. (with honors, Co-Op) and M.A.Sc. degrees in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 2007 and 2009 respectively, and is currently working toward the Ph.D. degree in electrical engineering at the University of Toronto, Toronto, ON, Canada. His M.A.Sc. degree research concerned novel dielectric resonator filters and system components. His current research interests include electromagnetics, periodic structures and metamaterials, antennas, and microwave structures/circuits. Mr. Memarian was the recipient of the Nortel Networks Scholarship, the Natural Sciences and Engineering Research Council of Canada (NSERC) Canada Graduate Scholarship (NSERC-CGS), and the Post-Graduate Scholarship (NSERC-PGS). He was also the recipient of the Honorable Mention Award of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) 2009 Student Paper Competition, as well as Best Oral Presentation Award of the IEEE MTT-S IMS 2009.

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George V. Eleftheriades (F’06) received the Diploma degree in electrical engineering from the National Technical University of Athens, Athens, Greece, in 1988, and the M.S.E.E. and Ph.D. degrees in electrical engineering from The University of Michigan at Ann Arbor, in 1989 and 1993, respectively. From 1994 to 1997, he was with the Swiss Federal Institute of Technology, Lausanne, Switzerland. He is currently a Professor with the Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada, where he holds the Canada Research Chair/ Velma M. Rogers Graham Chair in Engineering. His work has been cited over 7000 times. Prof. Eleftheriades has been a Fellow of the Royal Society of Canada since 2009. He was an IEEE Antennas and Propagation Society (IEEE AP-S) Distinguished Lecturer (2004–2009) and a member of the IEEE AP-S Administrative Committee (AdCom) (2008–2010). He is a member of the Technical Coordination Committee MTT-15 (Microwave Field Theory). He is an associate editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. He was the general chair of the 2010 IEEE International Symposium on Antennas and Propagation and CNC/USNC/URSI Radio Science Meeting, Toronto, ON, Canada. He was the recipient of the 2008 IEEE Kiyo Tomiyasu Technical Field Award, the 2001 Ontario Premiers’ Research Excellence Award, the 2001 Gordon Slemon Award presented by the University of Toronto, and the 2004 E. W. R. Steacie Fellowship presented by the Natural Sciences and Engineering Research Council of Canada (NSERC). He was the corecipient of the inaugural 2010 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS’ Best Paper Award and the 2008 and 2012 RWP King Best Paper Award.

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Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs Raúl Rodríguez-Berral, Carlos Molero, Francisco Medina, Fellow, IEEE, and Francisco Mesa, Senior Member, IEEE

Abstract—This paper presents a fully analytical model to determine the transmission and reflection properties of planar 1-D distributions of metal strips or slits made in thin metal screens. In contrast with other analytical or quasi-analytical approaches, the formulation incorporates the presence of dielectric slabs and is valid over a wide frequency band, from the long wavelength limit to the grating lobes operation. The model has been adapted to the case where two 1-D planar grids are stacked or a single grid is printed on a grounded substrate. In these cases, the model rigorously takes into account higher order mode interaction between the two stacked arrays of strips/slits or with the ground plane. Oblique incidence and both TE and TM polarizations have been considered. The analytical results show a good agreement with those computed by high-performance numerical methods, accounting for very fine details of extremely complicated transmission/reflection spectra. These results are of straightforward application to a variety of practical situations from microwaves to the terahertz regime. The present methodology can still be useful at higher frequencies provided that adequate models of the planar conductors are incorporated. In general, the model provides physical insight on the nature of the expected spectra and facilitates the design of devices based on planar metallic gratings. Index Terms—Diffraction gratings, equivalent-circuit model, extraordinary and conventional transmission/reflection, impedance matching.

I. INTRODUCTION

T

HE ANALYSIS of the electromagnetic response of periodic distributions of metallic planar scatterers (or planar apertures made in a metallic flat surface) has been a topic of interest for decades. This type of structure finds applications at very different frequency ranges, from the microwave and millimeter-wave bands (frequency-selective surfaces [1], polarizers [2], [3], artificial magnetic conductors [4], high-impedance surfaces [5], or partially reflective surfaces [6], just to mention a few examples) to the optical regime Manuscript received July 10, 2012; revised September 24, 2012; accepted September 25, 2012. Date of publication November 21, 2012; date of current version December 13, 2012. This work was supported by the Spanish Ministerio de Ciencia e Innovación and European Union FEDER funds under Project TEC2010-16948 and Project Consolider CSD2008-00066 and by the Spanish Junta de Andalucía under Project P09-TIC-4595. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. R. Rodríguez-Berral, C. Molero, and F. Mesa are with the Microwaves Group, Department of Applied Physics 1, Escuela Técnica Superior de Ingeniería Informática, University of Seville, 41012-Seville, Spain (e-mail: [email protected]; [email protected]; [email protected]). F. Medina is with the Faculty of Physics, Department of Electronics and Electromagnetism, University of Seville, 41012-Seville, Spain (e-mail: medina@us. es). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2224668

Fig. 1. Schematic representation of the problems under study. TM and TE polarizations and oblique incidence of the impinging wave are considered. (a) Slit-like 1-D planar grating with a stratified dielectric medium. (b) Strip-like 1-D planar grating in the same stratified environment.

[7]–[9], including infrared [10], [11] and terahertz applications [12], [13]. Apart from the technological interest of the practical applications of those structures, scientific curiosity has also triggered a lot of research on periodic planar or quasi-planar structures since the advent of extraordinary optical transmission [14]–[16]. The simplest geometry of the kind discussed above consists of an infinite 1-D periodic array of planar metal strips. As shown in Fig. 1, the strips could be embedded in a multilayered dielectric environment. In spite of its simplicity, this structure has been employed in different applications and frequency ranges, even in very recent studies [6], [9], [17]–[21]. Due to its geometrical simplicity, the structure can be analyzed with numerical methods allowing for a high degree of analytical preprocessing [22]. Under certain restrictions, it is possible to develop analytical or quasi-analytical methods, such as those found in [23]–[25]. Some of the authors of this paper have recently introduced an equivalent-circuit model involving lumped elements and transmission lines that removes many of the limitations encountered by previously developed analytical approaches [26], [27]. The same kind of model has also been used to explain an interesting phenomenon exhibited by strip-like structures under TE illumination [28], [29]

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RODRÍGUEZ-BERRAL et al.: ANALYTICAL WIDEBAND MODEL FOR STRIP/SLIT GRATINGS

(anomalous extraordinary transmission) or to design a terahertz polarizer [30]. The model is based on the idea of considering each unit cell of the periodic structure as a virtual parallel-plate waveguide discontinuity problem. This point of view is explicitly used in [31] and [32] to generate the numerical model and, to the authors’ knowledge, the first wideband circuit model approach is fully developed in [33]. In that paper, a few parameters (such as the values of lumped capacitors and inductors) were numerically obtained from full-wave solutions at a reduced number of frequency points. The approach in [27] for strip-like structures loaded with dielectric slabs took a step further in the analytical path, but still needed the numerical computation of one lumped component. The formulation in [27] started with a simplified mode matching scheme where a number of reasonable approximations were included. Our first aim in this paper is to eliminate the need for any kind of numerical simulations and to extend the scope of the work previously presented in [34]. This is done by starting with an integral-equation formulation for the electric field along the slits or for the electric current supported by the metal strips. If a reasonable assumption for those quantities is done, the proposed procedure leads to a fully analytical model (readily cast in the form of an equivalent circuit), where all the parameters are known in closed form. In contrast with other intuitive circuit-like approaches, lumped capacitors (inductors) do not necessarily coincide with the electrostatic (magnetostatic) values since frequency-dependent information associated with the lowest order scattered TE/TM modes is explicitly extracted out. This procedure leads to a very wideband equivalent circuit that is valid from zero frequency up to frequencies above the onset of the first few grating lobes. This is true for any angle of incidence provided the slits or the strips are electrically narrow. Apart from its fully analytical nature, another significant advantage of the formulation presented in this paper (with respect to the most closely related previous development in [27] and [34]) lies on its ability to deal with conductor backed strip/slit-like structures or with two stacked identical gratings. The interaction between two closely spaced gratings or the interaction of a single grating with a ground plane is accurately incorporated to the model. This has been done by considering all the relevant modes involved in the interaction, and not only the fundamental mode as it has been commonly done (see, e.g., [35]). A number of examples will illustrate the accuracy and wideband behavior of the proposed analytical model. The analytical results will be compared with a highly accurate and numerically efficient integral-equation formulation using full domain basis functions that incorporate the actual physical edge behavior.

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Fig. 2. (top) Unit cell corresponding to a periodic structure consisting of a periodic array of electrically narrow slits. (bottom) Circuit model to account for the scattering coefficients of the impinging electromagnetic wave.

a dielectric layer. Thus, if we consider the structure depicted in Fig. 2, and assume an implicit time–harmonic dependence of the type , the transverse electric field at the screen can be expanded in a Floquet series of spatial harmonics as (1)

where the amplitude of the impinging wave has been normalized to unity, is the reflection coefficient of the zeroth harmonic, is the tangential-to-the-grating component of the wave vector of the obliquely incident plane wave (in the present case, , with ), and . In the following, we will suppress the range of the index in the summation if it is from to . Since the electric field is continuous across the dielectric interface and zero on the perfect conducting screen, the same expansion coefficients are valid at both sides of the grating, which implicitly implies with being the transmission coefficient. The transverse magnetic field at both sides of the grating [ and ] is then given by (2) (3) where TE harmonics (4)

II. DERIVATION OF THE ANALYTICAL MODEL The derivation of the equivalent-circuit models here proposed follows a rationale similar to [27], but is based on an integralequation approach instead of a mode-matching scheme. First we derive the circuit model for a single grating placed between two different dielectric half spaces and later the presence of dielectric layers (see Fig. 1) is incorporated in the model by cascading transmission line sections, each of which corresponds to

TM harmonics is the transverse (with respect to ) wave admittance of the th harmonic in the th medium with (5) being its propagation wavenumber along . Next we consider separately the cases of slit and strip gratings.

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A. Slit Gratings If we denote the transverse electric field at the slit aperture as , the coefficients of the electric field expansion in (1) can be obtained by standard Fourier analysis as

(6) (7) where the tilde over the slit field denotes Fourier transform. From the above equations, we can write

of the equivalent circuit admittance (11) since this admittance only depends on the ratio of to . It is interesting to note that this procedure to find the equivalent admittance could be viewed, after using (12) in (9), as a method-ofmoments solution (with a Galerkin testing scheme) of the magnetic field integral equation for the slit aperture when using one single basis function, , for the unknown magnetic current (electric field) at the slit. For TM polarization, a suitable choice for the field profile is (13) and for TE polarization,

(8) which relates the coefficient of every spatial harmonic with the reflection coefficient. Now the continuity of the magnetic field through the slit is projected over the electric field at the aperture to obtain (9) where the asterisk indicates the complex conjugate. Introducing the expansions of the magnetic field in (2) and (3) into (9), we find the following expression for the reflection coefficient: (10)

(14) where represents the Bessel function of the first kind and order . These field profiles incorporate the proper (singular or zero) behavior of the field at the slit edges in each case. In the quasi-static limit, it is important to realize that the equivalent-circuit admittance in (11) can be conveniently approximated as (15) where it has been assumed that

. This allows us to write

where

(16) (11)

is identified as the global admittance of the equivalent circuit in Fig. 2. This admittance indicates that the equivalent circuit consists of a parallel connection of the wave admittances of the higher order spatial harmonics at both sides of the metallic grating, multiplied by a factor related to the spatial spectrum of the field profile at the slit (this factor could be interpreted as a transformer ratio). Unlike [27], these factors can now incorporate the a priori knowledge of the approximated field profile in the aperture (in [27] these factors were independent of as well as the incidence angle). Although (11) is a rigorous expression that is valid at any given frequency and for any slit width, in principle it is of little practical use unless the electric field at the slit aperture is known. Fortunately, for electrically narrow slits, we can make the reasonable assumption that the aperture field is given by (12) where is a frequency-dependent complex amplitude. This assumption implies that the spatial profile of the aperture field remains invariant in the frequency range of interest (in our experience, this condition is well satisfied up to the limit ; no specific restrictions are imposed on the period and the angle of incidence). Note that does not appear in the final expression

(17) and also [taking into account (4)] TE harmonics (18) TM harmonics The above derivation implies that the equivalent quasi-static admittance can be expressed in terms of a lumped inductance/capacitance (for TE/TM harmonics) given by the following frequency-independent series: (19)

(20) Thus, (19) and (20) provide analytical expressions of the quasi-static inductance/capacitance of a narrow-slit grating under TE/TM incidence. These lumped quasi-static elements can be used in simple models for dense gratings where the period is much smaller than the wavelength (see, e.g., [5]). However, as frequency increases, it is clear that the contribution of the first harmonics to the equivalent admittance of the grating

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Fig. 3. Proposed equivalent network for the slit grating in Fig. 2. (a) TM polarization. (b) TE polarization.

starts to deviate from its quasi-static behavior. Therefore, in order to improve the above approximation so that it can be employed beyond the quasi-static limit, we propose to express the equivalent admittance as follows (see Fig. 3):

Fig. 4. Equivalent network for a TM wave impinging obliquely from the left on a printed slit grating, .

TM polarization TE polarization

(21)

The first series in (21) explicitly takes into account the frequency dependence of the dominant harmonics, whereas the last term in (21) is an admittance that incorporates the effect of all the scattered harmonics of order in the form of a lumped frequency-independent inductance/capacitance . This “high-order” inductance/capcitance is given by the same series as in (19) and (20), but now the sum starts from . In our experience, the approximation (21) provides sufficiently accurate values if is taken as 1 plus the number of propagative harmonics in the medium with highest permittivity. In most practical cases, it implies that is rarely greater than 3 or 4. The presence of dielectric slabs in the structure under study is taken into account by introducing the corresponding transmission-line sections. The wave admittances in (11) and elsewhere should then be replaced by the input admittances to the corresponding cascade of transmission lines seen from the grating to the left and right ( and ). In order to clarify this point, Fig. 4 shows an example of the circuit model for a printed slit grating under TM incidence ), with the abovementioned input admittances schematically represented at the bottom. The parameters of this equivalent network are given by

Fig. 5. Unit cell corresponding to a periodic structure consisting of a periodic array of electrically narrow strips.

(25) Note that (24) is the resulting transformed admittance when the “load” admittance corresponding to the th harmonic of the right-most transmission line, , is viewed through a length of transmission line characterized by and . The expression of the high-order capacitance in (25) can be readily obtained after introducing the approximations (16) and (17) in the expressions of the input admittances of the harmonics of order higher than . B. Strip Gratings

(22) (23) (24)

In the situation shown in Fig. 5, we start by considering the surface current on the strips, which is denoted as . This surface current must equal the discontinuity of the transverse magnetic field, namely, (26)

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Using the magnetic field expansions (2) and (3), the above expression can be written as (27) (28) from which it is obtained that (29) Using the electric field integral equation, (30)

Fig. 6. Equivalent network for a TM wave impinging obliquely from the left on a printed strip grating, .

and after making the same assumption as in (12), but now for , we finally find that

TE polarization TM polarization

(31)

where the high-order inductance and capacitance are now given by (32)

(33) It should be noted that now the surface current profile is given by (14) for TM polarization and (13) for TE polarization of the impinging wave. The inclusion of dielectric layers can be done in a parallel way as that explained for the slit case. As an example, we can consider the case of a TM wave impinging on a printed strip shown in Fig. 6 . The equivalent network is also shown in the figure. The network parameters , , and are given by the same expressions in (22)–(24), respectively, although with appropriate profile . The high-order capacitance is given by

Fig. 7. Schematic representation of the coupled slit and strip gratings under analysis. The TE and TM oblique incidences are also represented on top. The optional electric wall condition at the middle plane accounts for the grating printed on a grounded slab, and also corresponds to the odd excitation of the coupled slit/strip gratings. The magnetic wall condition corresponds to the even excitation.

two cases of TE and TM oblique incidence. The structure shown at the top represents a pair of 1-D periodic array of slits made in an infinitely thin metallic screen printed on both sides of a dielectric slab (this structure can also be seen as a pair of coupled wide-strip gratings). The quasi-complementary problem involving strip gratings is shown at the bottom. The structures under study show a symmetry plane at the middle of the slab. This symmetry plane allows us to decompose the impinging excitation as the superposition of even ( ) plus odd ( ) excitations. Under even/odd excitation, this symmetry plane behaves as a magnetic/electric wall. The scattering parameters of the coupled structures can readily be found from the scattering parameters of the structures with even/odd excitations as (35) (36)

(34) III. MODEL FOR COUPLED GRATINGS In this section, we extend the previous circuit models to study the case of symmetric coupled gratings. The structures under consideration are sketched in Fig. 7, which also illustrates the

The case of a grating printed on a grounded slab is implicitly considered in this analysis since it is equivalent to the electric wall boundary condition at the middle plane of the dielectric slab. Next we present in some detail the derivation of the circuit model for the particular case of a strip grating printed on a grounded dielectric slab under TE incidence. The derivation for

RODRÍGUEZ-BERRAL et al.: ANALYTICAL WIDEBAND MODEL FOR STRIP/SLIT GRATINGS

Fig. 8. Equivalent network to model the slit grating printed on a grounded slab under TE polarization. The short-circuit termination accounts for the presence is the global impedance of the of the ground plane. The shunt impedance equivalent circuit that models the effect of the periodic grating.

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Fig. 9. Equivalent network for a strip grating printed on a grounded slab under normal TE incidence. Only the first element is explicitly taken into account with . its complete frequency dependence

TM incidence and for the slit grating under TE/TM incidence can be carried out along similar lines and will not be explicitly shown. Thus, we consider the strip grating in Fig. 7 with the electric wall condition (ground plane) at the middle. Following the approach discussed in Section II, the equivalent-circuit model of this structure is that depicted in Fig. 8. The transmission lines to the left and right of account for the propagation of the zeroth-order harmonic (incident and reflected wave) in free space and inside the dielectric, respectively. The short-circuit termination accounts for the presence of the ground plane, and the shunt impedance represents the global impedance of the equivalent circuit that models the periodic screen, which is given by

TE polarization TM polarization

(37)

where (38) In the particular case that and normal TE incidence, we find that the equivalent circuit reduces to that shown in Fig. 9, where it has been taken into account that , and therefore, the admittances of the and harmonics are identical and can be included in a single series element. The coefficient in Fig. 9 corresponds to (22) with , and the inductance is given by (39) For the case of a magnetic wall boundary condition, the derivation is completely analogous, but an open circuit should be considered instead of the short circuit in Fig. 8, and therefore, should be replaced with in (38). Also, in the particular case of the inductance in (39), should be replaced with .

Fig. 10. Magnitude of the transmission coefficient under TM oblique incidence embedded between two dielectric layers with of a slit grating , , , . Both dielectric layers are lossy . (a) Circuit model results. (b) MoM results. Normalized with . frequency

IV. NUMERICAL RESULTS AND DISCUSSION The analytical model proposed in this paper has been developed on the basis of a certain number of assumptions concerning the width of slits (or strips) and the field distribution (current distribution) on those slits (strips). Moreover, some decisions have to be taken before generating numerical results concerning the number of TE/TM harmonics of relatively low order that must be explicitly retained in the formulation (the information of the remaining infinite higher order modes is summarized by the lumped elements). However, these issues have been treated in detail in our previous paper on the same topic [27]. One of the main differences between this paper and [27] lies in the development of a fully analytical circuit-like model

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Fig. 11. Magnitude of the transmission coefficient under TE oblique incidence embedded between two dielectric layers with of a slit grating , , , and . Both dielectric layers . (a) Circuit model results. (b) MoM results. Norare lossy with . malized frequency:

(the lumped parameters in [27] were extracted from a numerical calculation for a single frequency point). In this paper, we have provided analytical formulas for all the relevant parameters, and it is necessary to check the accuracy of such formulas. However, the physical considerations about the number of modes that have to be retained to account for the (possibly) complex frequency-dependent behavior of the discontinuities are exactly the same as in [27]. The criterion here is to retain all the TE/TM harmonics that are above cutoff inside the highest dielectric constant slab plus the first evanescent higher order mode. Since the cutoff frequencies of the TE/TM harmonics are known in advance, this task can readily be implemented in the computer code. It should be noted that the relative weights of the modes calculated in [27] and in this paper are slightly different, with the ones in this paper being more accurate. As a validation of our present approach, we have recalculated with the new analytical formulation all the results already reported in [27] with an excellent agreement (these comparisons will not be explicitly shown). For further validation purposes, our results have also been compared with numerically generated data. A method of moments (MoM) in the spectral domain has been used to solve for the electric-field/surface-current integral equations for the slits/strips arrays. A sufficient number of entire-domain quasi-orthogonal basis functions that include the edge singularities have been employed to ensure high accuracy and fast convergence. The numerical results thus obtained

Fig. 12. Phase of the reflection coefficient for a strip grating printed on a lossless grounded slab under normal TE incidence. Structure parameters: , , . (a) . (b) . (c) .

for the scattering coefficients are accurate within 4–5 significant figures at least. Differences between analytical and numerical data cannot be appreciated in the plots provided the width of the slits/strips is small in comparison with the wavelength (roughly ). A very relevant fact is that the analytical model perfectly captures all the details of the transmission/reflection spectra: no peaks/dips are lost even for extremely complicated spectra exhibiting a large number of peaks/dips. In contrast with a model based on the excitation of surface waves [16], not only the frequency position of the peaks is almost exactly reproduced, but also the amplitude and phase at the peaks and at any other frequency over a very wide band.

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Fig. 13. Phase of the reflection coefficient for a strip grating under TE incidence and a slit grating under TM incidence, both printed on a grounded dielectric slab (electric wall at the middle plane in Fig. 7). Solid lines: results provided by a MoM numerical code. Circles and squares: results obtained with our circuit model. , , . (a) Incidence angle . (b) Incidence angle . (c) Incidence angle . (d) Incidence Structure parameters: . angle

In order to have a global idea about the performance of the model (although more detailed evidences can be found in [27]), we have included in Figs. 10 and 11 several illustrative color maps. These maps show the magnitude of the transmission coefficient for a couple of example structures as a function of the normalized frequency and the angle of incidence. Fig. 10(a) has been generated with the analytical model in this paper, and corresponds to TM wave incidence on a grating of narrow slits sandwiched between two different slightly lossy dielectric slabs. The numerically generated (MoM) results have been plotted in Figs. 10(b). The two plots are almost identical. The spectrum for high frequencies is very complex due to the presence of the dielectric slabs. Note that these kinds of plots are closely related to the Brillouin dispersion curves of the quasi-bound modes supported by the dielectric slabs periodically loaded with metal strips. It is worth mentioning that the explanation of the transmission peaks and zeros has been given, especially within the optics community, in terms of the interaction of the impinging TEM wave with the aforementioned quasibound modes (these modes were called spoof surface plasmons [36] due to their resemblance with the genuine surface plasmons supported by dielectric/solid plasma interfaces). The computa-

tion of these Brillouin dispersion curves is usually carried out by numerically solving an eigenvalue problem that demands a lot of computational effort. In contrast, the plot in Fig. 10(a) was generated in seconds thanks to the analytical nature of the model. Similar plots for a TE illuminated slit-like planar metal grating are shown in Fig. 11. A wider slit is considered here in order to enhance the high transmission frequency regions. Once again, the agreement between the numerical results and the analytical data is very good. In these figures, a narrow high transmission peak in the frequency range going from to (depending on the angle of incidence) can be clearly appreciated. Immediately after this peak, a transmission zero appears (Fano-like resonance). This is the so-called anomalous extraordinary transmission [28], [29]. For this polarization and grating geometry, low transmission regions rather than transmission peaks should be expected in the absence of electrically thick dielectric layers. It is the presence of dense dielectric slabs what introduces the possibility of having transmission peaks in an otherwise mostly opaque screen. The qualitative explanation for this phenomenon was discussed in [27]. Previously we have considered structures similar to those studied in [27] with the difference of using the new analytical

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Fig. 14. Transmission coefficient magnitude for: (a) TE and (b) TM illumination of two coupled arrays of narrow slits and (c) TE and (d) TM illumination of two . Structure parameters: , , , , , coupled arrays of narrow strips. The incidence angle is for all the layers.

tool. Now we consider conductor-backed or double-side structures for which no model was reported in [27]. This kind of structure can be studied in an approximate manner by using a lumped circuit component to account for the grating capacitance (TM case) or inductance (TE case) and a transmissionline section (with a short-circuit or an open-circuit termination) representing the grounded dielectric slab or the dielectric slab with a magnetic wall (symmetrical double-sided structures under even excitation conditions). This approach can be found, for instance, in [5] and [35]. Note that this transmission-line model only accounts for the fundamental TEM-like mode propagating inside the dielectric slab, and moreover, it does not consider the influence of the ground plane on the value of the lumped component. Thus, this representation ignores the possibility of higher order mode interaction of the grating with the ground plane (conductor-backed geometries) or with one adjacent identical grating (two-sided structures). At low frequencies, the higher order mode interaction can be ignored in practice if the dielectric slab is relatively thick or the value of is extremely small. However, significant differences between the analytical model and exact numerical calculations can be found in other cases. Furthermore, if the operation frequency is close or higher than the cutoff frequency of the first high-order harmonic inside the dielectric slab, then the coupling through this harmonic can strongly change the response

of the structure. Certainly, this effect cannot be taken into account by simple quasi-static models. As was explained earlier, our model incorporates all the interactions by splitting the discontinuity (grating) influence into two contributions: the frequency-dependent contribution linked to the scattered low order TE/TM modes and the frequency-independent contribution of the high-order modes. If we make in our formulation, our model reduces to a quasi-static model similar to the above mentioned simpler approach [5], [35]. Actually, with , we still keep the influence of the ground plane (or adjacent grating) on the quasi-static parameters characterizing the discontinuity, but this cannot account for the coupling through propagative harmonics at higher frequencies. To clarify this point, we compare the results obtained for an specific structure (strip grating printed on a grounded lossless slab) under normal TE illumination for several values of . Since the amplitude of the reflection coefficient is unity, we only plot the phase of the reflection coefficient in Fig. 12. Although the quasi-static model gives accurate results up to , noticeable differences can be appreciated above that frequency. Indeed, the results provided by the quasi-static model are qualitatively incorrect for . However, if the first two relevant higher order modes are explicitly taken into account (i.e., they are not considered as part of the higher order lumped contribution), the analytical model perfectly captures the details of the phase be-

RODRÍGUEZ-BERRAL et al.: ANALYTICAL WIDEBAND MODEL FOR STRIP/SLIT GRATINGS

havior up to the frequency of the onset of the first grating lobe. The model is still valid above that frequency but, in such a case, the magnitude of the specular reflection coefficient is not unity (depending on the operation frequency, parameter could need to be increased). Next, Fig. 13 shows the phase of the reflection coefficient versus normalized frequency for strip/slit gratings printed on a grounded dielectric slab (see the caption for the structure parameters). The MoM numerical results are also shown, and the comparison with the analytical results shows an excellent agreement for all the cases. It is well known that, as frequency increases, these structures present a near-zero phase for the reflection coefficient (artificial magnetic conductor) in a given frequency range. In the normal incidence cases considered in Fig. 13(a), this behavior occurs around for the strip grating under TE illumination and around for the slit grating under TM illumination. These values remain approximately the same for the oblique incidence results shown in Figs. 13(b)–13(d). For the high-frequency portion of the spectrum, the phase exhibits a faster and more complicated variation with frequency, especially for oblique incidence. As a final example, we have computed the transmission coefficient through a pair of symmetric coupled gratings printed on a thick substrate and sandwiched between two thinner dielectric slabs. The analytical and numerical results are compared in Fig. 14 for four different situations. The plots in Fig. 14(a) and (b) correspond to a pair of coupled slit-like (narrow slits) gratings under oblique TE and TM illuminations. The plots in Fig. 14(c) and (d) correspond to a pair of coupled strip-like (narrow strips) gratings under TE and TM illuminations. We can observe a very good agreement between numerical and analytical results in spite of the complexity of the transmission spectra. It is worth mentioning that simple circuit models that substitute the central dielectric slab with a TEM transmission line cannot be used when the operation frequency is close or above the cutoff frequencies of some of the first higher order TE or TM harmonics in the dielectric region. However, this is not an issue for our procedure. Finally, we should mention that, for wider strips, the results are slightly worse in the high-frequency part of the spectrum, but still acceptable for most practical purposes. V. CONCLUSIONS We have reported a fully analytical method to compute the transmission and reflection characteristics of strip- and slit-like diffraction gratings over a very wide frequency band (provided the strip/slit width is electrically small). The topology of the equivalent-circuit model and the values of their parameters (lumped capacitors/inductors and transmission lines) are extracted from a rigorous integral-equation formulation provided some reasonable approximations are employed. The proposed equivalent-circuit model can be seen as an alternative form of the integral-equation problem with the advantage that it provides more physical insight than the direct mathematical equations. Although other circuit-like models are available in the literature, the model here proposed systematically takes into account dynamic effects that are not usually accounted for. These effects are relevant at high frequencies, as well as

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when the metal gratings are close to a ground plane or strongly coupled to another identical grating, cases that have been specifically considered in this paper. The proposed model is useful to accurately characterize this kind of structures in classical microwave/millimeter-wave applications and to explain exotic phenomena recently reported in the optics and terahertz domains. REFERENCES [1] B. A. Munk, Frequency Selective Surfaces: Theory and Design. New York: Wiley, 2000. [2] B. Gimeno, J. L. Cruz, E. A. Navarro, and V. Such, “A polarizer rotator system for three-dimensional oblique incidence,” IEEE Trans. Antennas Propag., vol. 42, no. 7, pp. 912–919, Jul. 1994. [3] G. F. Brand, “The strip grating as a circular polarizer,” Amer. J. Phys., vol. 71, pp. 452–456, 2003. [4] M. A. Hiranandani, A. B. Yakovlev, and A. A. Kishk, “Artificial magnetic conductors realised by frequency-selective surfaces on a grounded dielectric slab for antenna applications,” Proc. Int. Elect. Eng.—Microw., Antennas, Propag., vol. 153, no. 5, pp. 487–493, Oct. 2006. [5] O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Risnen, and S. A. Tretyakov, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag., vol. 56, no. 6, pp. 1624–1632, Jun. 2008. [6] A. Foroozesh and L. Shafai, “On the characteristics of the highly directive resonant cavity antenna having metal strip grating superstrate,” IEEE Trans. Antennas Propag., vol. 60, no. 1, pp. 78–91, Jan. 2012. [7] G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negativeindex metamaterial at 780 nm wavelength,” Opt. Lett., vol. 32, pp. 53–55, 2007. [8] J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett., vol. 99, 2011, Art. ID 181120. [9] P. Patoka, T. Sun, M. Giersig, Z. Ren, and K. Kempa, “Nanoribbon plasmonic gratings and their anomalous interaction with electromagnetic waves,” Adv. Mater., vol. 24, pp. 3042–3045, 2012. [10] R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys., vol. 7, pp. 37–55, 1967. [11] R. Ulrich, “Effective low-pass filters for far infrared frequencies,” Infrared Phys., vol. 7, pp. 65–74, 1967. [12] M. E. MacDonald, A. Alexanian, R. A. York, Z. Popović, and E. N. Grossman, “Spectral transmittance of lossy printed resonant-grid terahertz bandpass filters,” IEEE Trans. Microw. Theory Techn., vol. 48, no. 4, pp. 712–718, Apr. 2000. [13] J. Carbonell, C. Croenne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys., vol. 108, 2010, Art. ID 014907. [14] T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature, vol. 391, pp. 667–669, Feb. 1998. [15] F. J. García-de-Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys., vol. 79, pp. 1267–1290, Oct.–Dec. 2007. [16] F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys., vol. 82, pp. 729–787, Jan.–Mar. 2010. [17] E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, C. Dupuis, S. Collin, F. Pardo, R. Haidar, and J.-L. Pelouard, “Free-standing guided-mode resonance and-pass filters: From 1-D to 2-D structures,” Opt. Exp., vol. 20, no. 12, pp. 13082–13090, Jun. 2012. [18] A. Khavasi, M. Miri, and K. Mehrany, “Surface plasmon-enhanced absorption in metal grating coupled terahertz quantum well photodetectors,” IEEE Trans. Terahertz Sci. Technol., vol. 1, no. 2, pp. 435–440, Nov. 2011. [19] X. Guo, R. Zhang, J. Cao, and H. Liu, “Surface plasmon-enhanced absorption in metal grating coupled terahertz quantum well photodetectors,” IEEE J. Quantum Electron., vol. 48, no. 9, pp. 1113–1119, Sep. 2012. [20] J. L. Perchec, Y. Desieres, N. Rochat, and R. E. Lamaestre, “Subwavelength optical absorber with an integrated photon sorter,” Appl. Phys. Lett., vol. 100, no. 9, Mar. 2012, Art. ID 113305.

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[21] M. Edalatipour, A. Khavasi, M. Rezaei, and K. Mehrany, “Creation of artificial surface conductivity on metallic metamaterials,” J. Lightw. Technol., vol. 30, no. 12, pp. 1789–1794, Jun. 2012. [22] K. Uchida, T. Noda, and T. Matsunaga, “Spectral domain analysis of electromagnetic-wave scattering by an infinite plane metallic grating,” IEEE Trans. Antennas Propag., vol. AP-35, no. 1, pp. 46–52, Jan. 1987. [23] M. Guglielmi and A. A. Oliner, “Multimode network description of a planar periodic metal-strip grating at a dielectric interface—Part I: Rigorous network formulations,” IEEE Trans. Microw. Theory Techn., vol. 37, no. 3, pp. 535–541, Mar. 1989. [24] M. Guglielmi and A. A. Oliner, “Multimode network description of a planar periodic metal-strip grating at a dielectric interface—Part II: Small-aperture and small-obstacle solutions,” IEEE Trans. Microw. Theory Techn., vol. 37, no. 3, pp. 542–552, Mar. 1989. [25] S. A. Tretyakov and C. R. Simovski, “Dynamic model of artificial reactive impedance surfaces,” J. Electromagn. Waves Appl., vol. 17, no. 1, pp. 131–145, Jan. 2003. [26] R. Rodríguez-Berral, F. Medina, and F. Mesa, “Circuit model for a periodic array of slits sandwiched between two dielectric slabs,” Appl. Phys. Lett., vol. 96, Apr. 2010, Art. ID 161104. [27] R. Rodríguez-Berral, F. Medina, F. Mesa, and M. García-Vigueras, “Quasi-analytical modeling of transmission/reflection in strip/slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 3, pp. 405–418, Mar. 2012. [28] M. Beruete, M. Navarro-Cía, S. A. Kuznetsov, and M. Sorolla, “Circuit approach to the minimal configuration of terahertz anomalous extraordinary transmission,” Appl. Phys. Lett., vol. 98, 2011, Art. ID 014106. [29] M. Beruete, M. Navarro-Cía, and M. Sorolla, “Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 9, pp. 2180–2188, Sep. 2011. [30] M. Navarro-Cía, P. Rodríguez-Ulibarri, V. Torres, and M. Beruete, “Quarter-wave plate based on dielectric-enabled extraordinary resonant transmission, concepts,” IEEE Photon. Technol. Lett., vol. 24, no. 11, pp. 945–949, Jun. 2012. [31] A. G. Schuchinsky, D. E. Zelenchuk, A. M. Lerer, and R. Dickie, “Full-wave analysis of layered aperture arrays,” IEEE Trans. Antennas Propag., vol. 54, no. 2, pp. 1490–502, Feb. 2006. [32] M. Beruete, I. Campillo, M. Navarro-Cía, F. Falcone, and M. Sorolla, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antennas Propag., vol. 55, no. 6, pp. 1514–1521, Jun. 2007. [33] F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 12, pp. 3108–3120, Dec. 2008. [34] R. Rodríguez-Berral, F. Mesa, and F. Medina, “Fully analytical circuitlike approach for the TE scattering by narrow-slit printed gratings,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [35] R. E. Diaz, J. T. Aberle, and W. E. McKinzie, “TM mode analysis of a sievenpiper high-impedance reactive surface,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Salt Lake City, UT, 2000, pp. 327–330. [36] J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science, vol. 305, pp. 847–848, Aug. 2004.

Raúl Rodríguez-Berral was born in Casariche, Seville, Spain, in 1978. He received the Licenciado (M.Sc.) and Ph.D. degrees in physics from the University of Seville, Seville, Spain, in 2001 and 2008, respectively. In January 2002, he joined the Department of Applied Physics 1, University of Seville, where he is currently an Assistant Professor. His research interests include the study of the spectrum and the excitation of periodic and nonperiodic planar structures and high-frequency circuit modeling.

Caros Molero was born in Las Navas, Seville, Spain, in 1987. He received the Licenciado degree in physics from the University of Seville, Seville, Spain, in 2011, and is currently working toward the Ph.D. degree in applied physics at the University of Seville. He is currently with the Department of Applied Physics 1, University of Seville.

Francisco Medina (M’90–SM’01–F’10) was born in Puerto Real, Cádiz, Spain, in November 1960. He received the Licenciado and Doctor degrees in physics from the University of Seville, Seville, Spain, in 1983 and 1987 respectively. He is currently a Professor of electromagnetism with the Department of Electronics and Electromagnetism, University of Seville, and Head of the Microwaves Group. He has coauthored approximately 120 journal papers. His research interest includes analytical and numerical methods for planar structures, anisotropic materials and artificial media modeling.

Francisco Mesa (M’93–SM’11) was born in Cádiz, Spain, in April 1965. He received the Licenciado and Doctor degrees in physics from the University of Seville, Seville, Spain, in 1989 and 1991, respectively. He is currently a Professor with the Department of Applied Physics 1, University of Seville. His research interests focus on electromagnetic propagation/radiation in planar structures.

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Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides Juan S. Ochoa and Andreas C. Cangellaris, Fellow, IEEE

Abstract—A methodology is presented for the fast electromagnetic analysis of the impact of statistical disorder on the transmission properties of periodic waveguides. The proposed methodology makes use of ideas from the Anderson localization theory to derive closed-form expressions for the calculation of an effective exponential decay ratio that quantifies the impact of periodicity disorder on the transmission properties of the waveguide. With regard to the quantification of the statistics of periodicity disorder from data obtained from a limited number of manufactured devices, a nonparametric probability density estimation process is examined and found to be satisfactory for our purposes. The computational efficiency of the proposed method over brute-force MonteCarlo-based alternatives is demonstrated through specific examples involving a periodically loaded parallel-plate waveguide. Furthermore, this numerical study is used to examine the accuracy of calculating the overall change in the propagation constant of the structure due to several sources of disorder as the sum of the changes calculated with each one of the sources of disorder considered individually. Index Terms—Disorder, finite element method, localization, Monte Carlo analysis, periodic waveguide, probability density estimation.

I. INTRODUCTION

P

ERIODIC waveguides are commonly used for a variety of filtering and other types of electromagnetic signal-processing applications [1]. Although these structures are intended to be ideally periodic, manufacturing-induced variability results in random alterations of the geometry and material properties of the structure. These, in turn, result in degradation of the intended transmission attributes of the electromagnetic structure. While Monte Carlo methods are the natural candidates for the quantitative assessment of the impact of such statistical variability on the electromagnetic attributes of the structure, their slow convergence is an issue of concern when the computational cost of the obtaining the response for each realization of the structure is high. Given the structures of interest, this is the case for our purposes, especially when three-dimensional (3-D) full-wave electromagnetic solvers are used. Thus, an alternative, more effiManuscript received July 09, 2012; revised September 22, 2012; accepted September 25, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under Grant W911NF-10-1-0269. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801 USA (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222917

cient approach is desirable. Such an approach is considered and evaluated in this paper. The proposed approach makes use of the Anderson localization theory [2] for the computationally efficient calculation of an average exponential decay per unit cell for the transmitted wave, also known in the solid state physics literature as localization factor. As already demonstrated through earlier applications of the Anderson localization theory to a variety of periodic dynamic systems (see, for example, [3]–[5]), this average exponential decay has been shown to provide for an accurate quantitative measure of the disorder-induced degradation of the response attributes of the periodic structure. In earlier studies, we have demonstrated how this technique can be used to analyze the effects of statistical material/geometric disorder in the electromagnetic properties of transmission-line-based metamaterial structures, where lumped circuit elements and transmission-line-based structures suffice for their modeling [6]. The way this methodology can be generalized for the case of periodic structures for which a full-wave, vectorial electromagnetic field formulation is needed for their modeling was presented in [7]. In this paper, we expand upon [7] to consider two important issues. The first one concerns the estimation of the probability density functions (PDFs) for the parameters that control geometric uncertainty for those cases that the only available information is in terms of a limited set of experimentally obtained data. The second issue concerns the way the impact of multiple sources of stochastic disorder on the transmission properties of the periodic structure can be handled in a computationally efficient and accurate manner. This paper is organized as follows. In Section II, we consider the uncertainty in the geometric/material disorder of the periodic structure and describe the method we adopt for its description in terms of a PDF given an appropriate set of experimentally obtained data. In Section III, we make use of the finite-element method (FEM) for the electromagnetic modeling of the structure and explain how the FEM model can be combined with the results in [5] to compute the localization factor for a disordered periodic structure. The accuracy of the proposed method, along with some of its key attributes, are examined in Section IV through its application to the analysis of a periodic waveguide. The paper concludes with a summary of the proposed methodology and a brief outlook of possible extensions and applications. II. QUANTIFICATION OF UNCERTAINTY IN INPUT PARAMETERS To fix ideas, consider the case of the -invariant, parallelplate waveguide structure of longitudinal section, as depicted in Fig. 1. Without loss of generality, we consider the case where

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Fig. 1. (a) Longitudinal cross section of a disordered periodic parallel-plate waveguide. (b) The disorder is caused by a random perturbation in the length of the unit cell.

Fig. 2. Estimated PDF obtained using a diffusion-mixing-based estimator and KDE using as input 30 randomly chosen samples that follow a Gaussian distribution.

all materials are lossless and the structure is operated at the fundamental, transverse electromagnetic (TEM) mode, with wave propagation along . The intended periodic loading with -directed conducting strips of rectangular cross section would result, under ideal conditions of perfect periodicity, in a band-stop filter structure. However, in the presence of uncertainty in the longitudinal positioning of each wire, such ideal behavior is degraded. For example, as depicted in the figure, an uncertainty in the length of the unit cell is readily described in terms of a single random variable, . To start with, we need to quantify the uncertainty in terms of the PDFs of the geometric parameters identified as the sources of the uncertainty. Once these PDFs are available, an electromagnetic model of the structure is required to propagate the input uncertainty to the electromagnetic response of the structure. The ultimate result is the quantitative prediction of the impact of input uncertainties on the transmission properties of the structure. A common practice is to assume that the input random parameters follow an arbitrary distribution, which is most often chosen to be either uniform or Gaussian. However, in several cases, the only information available for the characterization of input uncertainty is a set of data obtained either from the direct measurement of the manufactured devices or from information pertinent to the uncertainty introduced by the manufacturing process. This then calls for a systematic way for the estimation of the PDF for an input random variable from a limited set of data. Without loss of generality, let us assume that input uncertainty is defined in terms of a finite number of independent random variables, and no correlation exists between random variables from one unit cell to the next. Following the measurement of these random parameters, an effective means for obtaining the PDF of each random variable from the available measured data by means of a nonparametric density estimation process is applied. The attractive attribute of such a process is that no assumption is made about the randomness of the input data. The method of choice for our purposes is the nonparametric diffusion-mixing-based estimator presented by Botev et al. [8], [9] and previously employed in the stochastic analysis of micro-electromechanical structures in [10] and [11]. The

method combines the traditional Kernel Density Estimation (KDE) process with the solution to a generalized diffusion equation for the unknown distribution with point sources associated with the available measured data. Utilizing position-dependent diffusivity and drift terms that are dependent on an estimate of the PDF, a position-dependent diffusion and drift are effected in the solution. More specifically, in regions where the estimated density is low and, thus, fewer observations are expected, a higher diffusion and drift provide for a smoothing of the initial data. In contrast, for those regions where higher values of the estimated density indicate a higher value of expected observations, the diffusion and drift are lower. The main disadvantage of using the diffusion model is the relatively long computational time. Solving a heat equation in the time domain is considerably more expensive and complex than the traditional KDE approach. However, considering the importance of starting with the right characterization of the random variable, this drawback is tolerable. Due to these attributes, the diffusion-mixing-based estimator has been shown to provide improved accuracy over KDE in the PDF estimate for any point in the interval spanned by the input data. This improved accuracy is demonstrated in Fig. 2, which compares the estimated PDF using standard KDE and the diffusion-mixing-based estimator using as input a set of 30 randomly chosen samples that follow a Gaussian random variable with zero mean and standard deviation 0.05. The attributes of the diffusion-mixing-based estimator is evident. In particular, the method captures the behavior of the random variable with higher accuracy in the peaks and valleys of the distribution. A summary of the key steps for the development of an algorithm for the diffusion-mixing based estimator is provided in the Appendix. III. ELECTROMAGNETIC MODEL UNCERTAINTY PROPAGATION

FOR

Next, we turn our attention to the development of a model for the propagation of the input data uncertainty to the electromagnetic response of the periodic structure. With the structure depicted in Fig. 1 as our reference structure, and under the

OCHOA AND CANGELLARIS: EXPEDIENT ELECTROMAGNETIC ANALYSIS OF THE IMPACT OF STATISTICAL DISORDER IN PERIODIC WAVEGUIDES

stated assumption that the structure is operated at the fundamental TEM mode with wave propagation along , the transmission properties of the structure are quantified in terms of the propagation constant of the TEM wave. In the case of an ideal structure that exhibits no disorder in its periodicity, the propagation constant can be computed through the application of Floquet analysis [1]. In such an analysis, the electromagnetic model involves the region associated with the unit cell of the periodic structure. Over this region, an approximation of Maxwell’s equations in the absence of sources is used to develop the numerical model used for the analysis of the electromagnetic properties of the periodic structure. For our purposes, the FEM is used for the approximation of Maxwell’s equations. In particular, the Floquet-based FEM in [12] is adopted. Through a standard Galerkin process, the finite-element approximation of the vector Helmholtz equation for the electric field over the unit cell of the periodic waveguide results in a linear system of the form (1) where

, and the entries of vectors are the weights of the expansion functions used to approximate the electric and magnetic fields on the left and right boundaries of the unit cell, respectively, which are perpendicular to the direction of wave propagation. Imposing the Floquet periodic boundary condition on these boundaries, where denotes the distance between the two boundaries for the case of the unperturbed unit cell, results in the linear eigenvalue problem (2) The solution to (2) yields a set of eigenvalues and their respective eigenvectors. With the bandwidth of interest of the electromagnetic analysis limited to TEM mode propagation only, the eigenmodes of interest are the ones for the TEM left-propagating and right-propagating waves. Their eigenvectors are sorted in the matrix . Next, consider a small disorder in the position of the wire in the th cell described in terms of a statistical variability in the length of the cell as follows:

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of (4) on the left by , where the superscript denotes complex-conjugate transposition, and inverting the resulting 2 2 matrix yields the transmission matrix relationship

(5) relates the modes on the left The transmission matrix boundary of the unit cell to the modes on its right boundary. Clearly, for the unperturbed unit cell the above equation is of the form (6) Finally, the assumption is made that the transmission matrix of the th perturbed cell can be expressed as the product of the ideal transmission matrix and a perturbation matrix [5] as follows: (7) for each realization of Since we can compute matrix the geometry in the random space and for the unperturbed case, matrix is computed directly from (7). With all of the aforementioned matrices defined, standard microwave network analysis techniques are used to calculate the transmission characteristics of a structure consisting of the cascade of cells exhibiting disorder. Under the assumption that cells with index exhibit no disorder, such an analysis may be used to obtain an effective propagation factor per cell that quantifies the transmission attributes of the structure and is defined as follows [5]: (8) where is the element (2,2) of the matrix that represents the overall transmission of a wave traveling from left to right from the input of perturbed cell 1 to the output of perturbed cell as

(9) (3) The random variable is assumed to follow a given probability distribution with zero mean and standard deviation . Furthermore, it is assumed that variables , one for each cell that exhibits disorder, are independent and identically distributed. In a manner similar to the case of the ideal unit cell, the FEM describing propagation through the th cell is of the form

While standard Monte Carlo analysis may be used for the calculation of the propagation factor in the presence of statistical variability, under the assumption of an infinitely long disordered period structure (i.e., for the case ), closed-form expressions for its calculation are possible under the assumption of small, moderate, and even strong reflections between adjacent cells, as detailed in [5]. In particular, for the case of small reflections, it is

(4) In the above equation, use was made of the fact that the vectors at the left and right ends of the th cell can be expressed in terms of the eigenvectors of the fundamental eigenmodes , where . Multiplying both sides

(10) where the subscript in is used to indicate that this value of the propagation constant is the one obtained under the

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assumption of small reflections. For the case of moderate reflections, the closed-form expression becomes

With

being the number of cells, the pertinent integral is (12)

is the vector of the random variables , that quantify the disorder in each unit cell and , which is their joint probability distribution. For the special case of , the above equation reduces to the small-reflections equation one [(10)]. An advantage of (12) is that we can prescind of assumption (7), necessary for the moderate-reflections approach presented by Cai. Instead of a brute-force Monte Carlo scheme, an efficient multivariate quadrature rule, based on the sparse Smolyak algorithm [13], [14], is employed for the numerical calculation of (12). In this manner, the approximation of (12) through the weighted sum of function evaluations where

(11) The subscript in indicates that this value of the propagation constant is the one obtained under the assumption of moderate reflections. In the above equations, denote the elements of the perturbation matrix defined in (7) above. Under the approximation of small reflections, it is understood that the impact of multiple reflections between adjacent cells can be assumed negligible. In this case, the integration in (10) is carried out over the random domain of , and it is done by using a quadrature rule. For such purposes, we need to perform a number of FEM simulations to compute matrix and its element for each node of a sparse grid in the random space. Once the samples of are found, we can approximate integral (10) with a simple weighted sum of evaluations of the integrand. The case of moderate reflections is understood to represent the situation where reflections between adjacent cells are not negligible and must be accounted for in the calculation of the perturbed propagation constant. Thus, in this case the random space is two-dimensional (2-D), defined in terms of the two random variables and in (11), associated with unit cells and , and contributing the impact of the inter-cell reflection to the value of the effective propagation factor. Since perturbation in one unit cell is assumed to be described by statistics independent from the perturbation in other cells, these two variables correspond to the same random variable and share the same distribution. Therefore, even though a 2-D quadrature rule is involved in this case for the calculation of the integral in (11), the points on the tensor grid utilized for this purpose involves the points of the one-dimensional (1-D) quadrature along each dimension. Thus, the matrix whose elements appear in (11) needs to be computed for the same values of the 1-D quadrature rule. Consequently, the same number of finite-element solutions is needed for the calculation of for both the case of small reflections and the case of moderate reflections. A. Chain of Unit Cells As already mentioned, (10) and (11) are meant to be used for structures of sufficiently large number of unit cells to approximate the case of an infinite disordered periodic structure. Their simplicity begs the question whether they can be used as approximations to the propagation factor per unit cell of finite disordered periodic structures involving a small number of unit cells. This possibility can be assessed in a straightforward fashion through the approximation of (8) by the mean value of for the case of the matrix computed from (9) for a finite structured involving a small number of cells.

(13) involves a number of nodes over the random space that is significantly smaller than the one involved in a tensor product grid and is determined by the Smolyak accuracy level. The details on the selection of the Smolyak grid nodes and the associated weights for a given level of accuracy can be found in [14]. The evaluation of (13) requires the computation of the transmission matrix for the chain of unit cells. From the point of view of the finite-element solution of this problem, the number of degrees of freedom in the discrete model for the entire structure is roughly times that of the discrete model for a single unit cell. Clearly, the computational cost of such an approach is significant, especially considering that the dimension of the random space is . Thus, a more computationally efficient alternative is desired. Such an alternative is offered by computing instead the transmission matrices of the single unit cells involved in the structure and then applying (9) to obtain the overall matrix for each realization of the structure in the random space. This approach allows us not only to reduce the computational cost associated with the finite element solution of the -cell structure, but also to reduce the number of solutions needed. More specifically, the assumption that the variables of each unit cell are identically distributed allows us to employ a multidimensional Kronrod–Patterson quadrature rule [14] whose -tuples nodes are different combinations of the nodes associated with a much simpler 1-D quadrature rule. Therefore, similarly to the calculation of the 2-D integral in (11), we only need to obtain finite-element solutions for the unit cell at the nodes of the 1-D grid. Thus, the bulk of computational cost of this alternative is approximately the same to the one for (10). IV. VALIDATION STUDIES Here, we use the presented methodology to compute the localization factor of the disordered waveguide as shown in Fig. 1. Its real part represents the exponential decay per unit cell that the wave suffers as it travels through the disordered structure. For its calculation using integrals (10) and (11), a 1-D

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Fig. 4. Simulation times of a MATLAB code running in a 2.50-GHz Xeon CPU machine per frequency point for chains of five, four, three, and one unit cells as a function of the sparse grid algorithm accuracy. Fig. 3. Localization factor for the periodic structure of Fig. 1, due to a random perturbation in the length of the unit cell following a Gaussian distribution of . zero mean and standard deviation of

quadrature rule with Smolyak accuracy of level 3 is utilized. Thus, the finite-element solver used to compute matrices for a single unit cell needs to be run only three times for each frequency, corresponding to the grid points in the random space given by the quadrature rule. This should be contrasted to the calculation of (13) with , where the finite-element solver for the four-cell disordered geometry had to be run 33 times for each frequency. Once the transmission matrices have been found and the corresponding distribution of the random variable characterized, the localization factor, is numerically computed with a summation as shown in (13). Referring to the geometry of Fig. 1, a structure with and was analyzed. A Gaussian random variable with zero mean and standard deviation 0.05 was employed to quantify the cell length disorder. Fig. 3 depicts the calculated decay per unit cell, plotted versus , where is the angular frequency and is the speed of light in vacuum. In the figure, a comparison is offered of the ideal case of a perfect periodic structure exhibiting zero attenuation in the passband, with results obtained using four different approaches: 1) the small-reflection formula (10) (black dashed lines); 2) the moderate-reflection formula (11) (gray asterisks); 3) the calculation of (13) for with the chain-of-cells approach (red circles); and 4) the calculation of (13) for with the overall transmission matrix obtained as the product of the four transmission matrices for the four unit cells with each cell modeled individually (white circles). As mentioned in the Introduction, we have previously considered the use of the ideas from Anderson localization to the expedient analysis of the impact of disorder of a transmissionline-based metamaterial on its transmission properties [6] and validated their accuracy using a brute-force Monte Carlo analysis. Because of the increased computational cost of brute-force Monte Carlo analysis when FEMs are necessary for the numerical analysis of the structures of interest, we have relied on the use of sparse grid sampling of the random space [15] for the Monte Carlo analysis of the four-unit-cell structure.

It is clear from Fig. 3 that the computed attenuation (real part of ) using (10) under the assumption of small reflections is in agreement with the results obtained from the more expensive calculation using (13) as well as the alternatives moderate reflections and matrix-concatenation approach, especially for frequencies to the left of the stopband. The simulation times of a MATLAB code running on a 2.50-GHz Xeon CPU Windows machine for the small reflections approach for different numbers of unit cells are compared in Fig. 4. The advantage of using a reduced number of unit cells in terms of computational time is evident. If higher accuracy is desired, the more computationally expensive approach (chain of unit cells) is recommended for use. Also depicted in Fig. 3 is the result from the evaluation of (10) using the distribution depicted in Fig. 2 that was estimated using the nonparametric diffusion-mixing based KDE from 30 randomly chosen samples (blue dotted line). It is evident from Fig. 3 that the computed results are in excellent agreement with the other approaches that use analytical Gaussian distribution for the random variable describing the disorder. This suggests that the proposed nonparametric diffusion-mixing-based KDE approach is a promising candidate for the description of uncertainty in input parameters from a limited set of experimentally obtained data. Fig. 5 depicts the average perturbation in the imaginary part of the propagation constant caused by the disorder for a range of standard deviation values. As expected, the cases with larger disorder, described in terms of a larger standard deviation, result in higher perturbation in the passband. While the real part of describes field attenuation per unit cell, the perturbation in the imaginary part of quantifies the resulting change in the phase shift per unit cell of the transmitted wave. V. CASE OF MULTIPLE RANDOM VARIABLES Thus far, our discussion has focused on the case where the disorder in the unit cell is described in terms of a single random variable. In the general case, several random variables may be required for the description of geometric and material uncertainty. Each of these variables contributes to the perturbation in

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Fig. 6. Case of a unit cell with two sources of disorder, namely, the width and the thickness of the -directed conducting strips.

Fig. 5. Perturbation in the imaginary part of propagation constant per unit cell for the periodic structure of Fig. 1, due to a random perturbation in the length of the unit cell following a Gaussian distribution of zero mean and standard 0.01, 0.05, and 0.1. deviation of value

the propagation factor per unit cell. The resulting perturbation can be computed using a slightly modified version of (12) as follows: (14) is a vector containing the random variables, , describing the random disorder. Assuming that these variables are independent, their joint PDF is simply the product of the PDFs. Again, by making use of a sparse grid integration algorithm, the number of full-wave simulations needed for the calculation of the integral over the random domain can be reduced. As an alternative to the aforementioned approach for calculating the change in the propagation factor per unit cell, Kissel proposed in [16] that the localization factor due to several sources of random disorder may be computed as the sum of the individual localization factors obtained by considering each source by itself as follows: where

Fig. 7. Real part of propagation constant per unit cell for the disordered structure of Fig. 6 involving two sources of random disorder.

(15) Clearly, the advantage of this alternative is that it results in a small number of finite-element solutions per frequency point, equal to , where is the number of nodes in a 1-D quadrature grid over the interval of each random variable. To examine the validity of this assertion, we consider the case of a periodic waveguide of the type depicted in Fig. 1 where the disorder in the unit cell is described in terms of two parameters, namely, the width and the thickness of the cross-sectional geometry of the -directed wires. More specifically, we have (16) (17) as shown in Fig. 6. In the above equations, , and the random variables follow Gaussian distributions with zero mean and standard deviations of 0.2 and 0.1, respectively.

Fig. 8. Imaginary part of the change in the propagation constant per unit cell for the disordered structure of Fig. 6 involving two sources of random disorder.

For the evaluation of (14), a 2-D Smolyak grid is utilized involving 37 points and accuracy level of 5. Thus, 37 finite-element solutions per frequency point are needed. In contrast, by considering separately each one of the two sources disorder and then adding up the calculated perturbations in the propagation factor to calculate the overall change according to (15), nine finite-element solutions per frequency point are required for each source. Figs. 7 and 8 contrast the results from the two approaches. Shown in Fig. 7 is the real part of the propagation constant per unit cell, plotted versus , while the imaginary part of the change in the propagation constant per unit cell is shown in 8. Very good accuracy is observed, supporting Kissel’s conjecture and the merits of (15) as an expedient, yet

OCHOA AND CANGELLARIS: EXPEDIENT ELECTROMAGNETIC ANALYSIS OF THE IMPACT OF STATISTICAL DISORDER IN PERIODIC WAVEGUIDES

accurate, means for computing the change in the propagation constant of the wave due to multiple sources of random disorder in the periodicity of the waveguide structure. VI. CONCLUSION In summary, a methodology has been presented for the calculation of the impact of random disorder in periodic electromagnetic waveguides on their transmission characteristics. Rather than using a Monte Carlo scheme where the entire structure, which may consist of several disordered unit cells, is solved using an electromagnetic field solver for each realization in the random space, the proposed method makes use of ideas from the Anderson localization theory to limit the numerical modeling to the unit cell only. More specifically, under appropriate conditions that are expected to hold in many of the applications of interest, closed-form expressions are used to calculate a disorder-induced attenuation factor per unit cell. The accuracy of these expressions has been assessed through the use of more general yet computationally more expensive models and has been found to be sufficient for the cases studied. Also addressed in the paper is the issue of the proper modeling of the random disorder in the structure for those cases where a PDF for its description is not readily available, and its modeling has to rely upon experimentally obtained data. For such cases, it was shown that the diffusion-mixing-based kernel density estimator of [9] can be used reliably to obtain the probability density function for the random variables that describe geometric uncertainty. For the case where the random disorder in the structure requires multiple random variables for its description, the possibility of computing the overall change in the propagation constant per unit cell as the sum of the changes computed by considering each random variable individually was examined. Very good accuracy was obtained for the structures considered, suggesting that such an approach has merit and should be used as a first option, especially for cases where the dimension of the random space describing the disorder is large. While the proposed method was demonstrated in the context of a 2-D waveguide, its extension to the general case of 3-D waveguides exhibiting periodicity along the direction of wave propagation is straightforward. It is emphasized that the electromagnetic modeling in the proposed approach relies upon the calculation of the transmission matrix for the unit cell of the structure, which, in turn, can be carried out using any appropriate electromagnetic field solver. The more challenging extension is the one where the interaction between adjacent cells requires the consideration of more than the fundamental mode of the structure. This is currently under investigation and will be presented in a forthcoming publication. APPENDIX DENSITY ESTIMATION For completeness, we present in this Appendix the key elements of the diffusion-mixing-based density estimation process of [8], [9]. For a more in-depth discussion of the method and its implementation, the reader is referred to the aforementioned

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references [10], [11] for specific examples from the application of the method to uncertainty quantification in the context of MEMS. The process starts with a set of measurements for a given random quantity for which no other information is available. In this sense, the method is general, applicable to any type of random variable; no further information other than the data is needed. It should be noted that, since the nature of the random variable is unknown, a simple estimation of its first and second moments is not sufficient to completely describe its distribution. To illustrate the process, we start with data obtained for a Gaussian random variable. The Gaussian PDF, with zero mean and standard deviation 0.05, used is shown in Fig. 2. Also shown, is the random set of samples used as our available set of data. Next, we proceed to find a first approximation of the distribution. For this purpose, we make use of the KDE method. KDE estimates the PDF by expressing the density as a linear combination of properly selected kernel functions centered at the data points [11]. Fig. 2 presents the KDE approximation, computed following the process presented in [10]. It is evident from the figure that the agreement between the KDE computed distribution and the actual PDF is deficient for the case of samples. Better agreement is obtained for sets of 300 or more samples. However, in practice, it is often the case that the number of available data is limited. Thus, there is a need for an alternative nonparametric method that provides better accuracy for those cases where a limited number of samples is available. The diffusion-mixing-based estimator of [9] provides for such a method. This is described next with the KDE used to provide an initial guess for the estimated PDF [10]. A. Diffusion Model for Density Estimation In the heart of this method is the idea that the PDF to be estimated can be computed as the solution of the generalized heat diffusion equation, given by (18) for . In the above equation, is a positive function in , and is the PDF describing any available prior information. The equation is solved in with boundary conditions . The meaning of these boundary conditions is obvious and physically satisfying: the estimated PDF is zero at the boundaries of the domain, because the range of the allowed values of the parameter under consideration is finite. For example, in the context of the specific example of a periodic waveguide considered in this paper, adjacent crossing loading wires in the waveguide are at a finite distance from each other and cannot coincide or partially superpose. Thus, the uncertainty in the distance between them is constrained to a certain range controlled by the intended attributes of the structure. Returning to the functions and , it is noted that they provide for smoothing of the density in regions where data is sparse and sharpening in regions of high concentrations of data [10]. Clearly, they have to be specified before the equation can be solved. As already mentioned above, in the absence of any

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a priori information about the PDF, its initial value is computed using standard KDE with a Gaussian kernel. Once obtained, is used for the calculation of and through the equations and . As it has been shown in [10], these choices with a relatively low value of minimize the mean integrated square error of the estimated distribution. For our purposes a value of is employed. Concerning the numerical solution of (18), a finite-difference time-domain formulation is used with initial condition taken to be a combination of Dirac delta functions placed at the samples as follows: (19) Similarly to KDE, the optimum value of the simulation time in the solution of (18) is chosen such that it maximizes the maximum-likelihood cross validation (MLCV) score

[8] Z. I. Botev, “Nonparametric density estimation via diffusion mixing,” Univ. of Queensland, Tech. Rep., Nov. 2007 [Online]. Available: http:// espace.library.uq.edu.au/view/UQ:120006 [9] Z. I. Botev, J. F. Grotowski, and D. P. Kroese, “Kernel density estimation via diffusion,” Ann. Statist., vol. 38, no. 5, pp. 2916–2957, 2010. [10] N. Agarwal and N. R. Aluru, “A data-driven stochastic collocation approach for uncertainty quantification in MEMS,” Int. J. Numer. Methods Eng., vol. 83, pp. 575–597, Mar. 2010. [11] A. Alwan and N. Aluru, “Uncertainty quantification of MEMS using a data-dependent adaptive stochastic collocation method,” Comput. Methods Appl. Mech. Eng., vol. 200, pp. 3169–3182, 2011. [12] Y. Zhu and A. Cangellaris, Multigrid Finite Element Methods for Electromagnetic Field Modeling. Hoboken, NJ: Wiley, 2006. [13] E. Novak and K. Ritter, “High dimensional integration of smooth functions over cubes,” Numerische Mathematik, vol. 75, pp. 79–97, 1996. [14] F. Heiss and V. Winschel, “Likelihood approximation by numerical integration on sparse grids,” J. Econometr., vol. 144, no. 1, pp. 62–80, May 2008. [15] D. Xiu and J. S. Hesthaven, “High-order collocation methods for differential equations with random inputs,” SIAM J. Sci. Computing, vol. 27, no. 3, pp. 1118–1139, 2005. [16] G. Kissel, “Localization in disordered periodic structures,” Ph.D. dissertation, Dept. Aeronaut. Astronaut., Mass. Inst. Technol., Cambridge, 1988. [17] R. Duin, “On the choice of smoothing parameters for parzen estimators of probability density functions,” IEEE Trans. Comput., vol. C-25, no. 11, pp. 1175–1179, Nov. 1976.

(20) where

is the solution of (18) with the initial condition (21)

which excludes the th sample [17]. Finally, results in Fig. 2 compare the two discussed nonparametric estimation methods with the actual normal distribution from which the sample points were chosen. As observed, the diffusion-mixing-based estimation exhibits superior accuracy to the traditional KDE, especially in the valleys and peaks of the distribution. REFERENCES [1] R. E. Collin, Foundations for Microwave Engineering. New York: McGraw-Hill, 1992. [2] P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev., vol. 109, no. 5, pp. 1492–1505, Mar. 1958. [3] G. J. Kissel, “Localization and the invariant probability measure for a structural dynamic system,” Modeling, Signal Process., Control for Smart Structures, vol. 7286, no. 1, Apr. 2009. [4] C. Pierre, “Weak and strong vibration localization in disordered structures: A statistical investigation,” J. Sound Vibration, vol. 139, no. 1, pp. 111–132, May 1990. [5] G. Cai and Y. Lin, “Localization of wave propagation in disordered periodic structures,” AIAA J., vol. 29, no. 3, pp. 450–456, Mar. 1991. [6] J. Ochoa and A. Cangellaris, “Analysis of the impact of statistical variations on transmission-line based metamaterial structures,” in Proc. Eur. Microw. Conf., Sep. 2010, pp. 1397–1400. [7] J. Ochoa and A. Cangellaris, “A methodology for expedient analysis of the impact of disorder in periodic waveguides,” in Proc Int. Microw. Symp., Jun. 2012, pp. 1–3.

Juan S. Ochoa received the B.S. degrees (summa cum laude) in physics and electrical engineering from the University San Francisco at Quito, Ecuador, in 2008, and the M.Sc. degree in electrical engineering from the University of Illinois at Urbana-Champaign, Urbana, in 2010, where he is currently working toward the Ph.D. degree in electrical engineering. He recently completed an internship at Intel as a Signal Integrity Engineer in the summer of 2011. His research interests include computational electromagnetics, stochastic model-order reduction, sparse grid methods, metamaterials, and electromagnetic scattering. Mr. Ochoa was a recipient of the Prof. Kung Chie Yeh Fellowship from the University of Illinois at Urbana-Champaign for outstanding scholastic record and contributions in wave propagation.

Andreas C. Cangellaris (F’00) received the Diploma from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 1981, and the M.S. and Ph.D. degrees from the University of California, Berkeley, in 1983 and 1985, respectively, all in electrical engineering. He is currently the M.E. Van Valkenburg Professor of Electrical and Computer Engineering with the University of Illinois at Urbana-Champaign (UIUC), Urbana. Prior to joining UIUC, he was on the faculty of the Department of Electrical and Computer Engineering, University of Arizona, from 1987 to 1997. His current research interests include computational electromagnetics, computeraided design methodologies and tools for high-speed/high-frequency electronic components and systems, EMI/EMC modeling and simulation, and modeling methodologies and tools for multidomain physics analysis. Prof. Cangellaris serves as Editor of the IEEE Press Series on Electromagnetic Field Theory. He is the cofounder of the IEEE Topical Meeting on Electrical Performance of Electronic Packaging in 1991, which, in its new form as the IEEE Symposium on Electrical Performance of Electronic Packaging and Systems, has established itself as one of the premier venues in the field of performance- and noise-aware electronic system integration. He is an active member of the IEEE Microwave Theory and Techniques Society (MTT-S) and has served as a Distinguished Microwave Lecture during 2008–2010. He serves currently as Chair of MTT-15 Technical Committee on Electromagnetic Field Theory. He also serves as editor of the IEEE Press Series on Electromagnetic Wave Theory. He is the recipient of the Alexander von Humboldt Research Award in 2005, the Army Research Laboratory Director’s Coin in 2011, and the IEEE MTT-S Distinguished Educator Award in 2012.

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Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach Muhammad Kabir, Student Member, IEEE, and Roni Khazaka, Senior Member, IEEE

Abstract—Recently, Loewner matrix (LM)-based methods were introduced for generating time-domain macromodels based on frequency-domain measured parameters. These methods were shown to be very efficient and accurate for lumped systems with a large number of ports; however, they were not suitable for distributed transmission-line networks. In this paper, an LM-based approach is proposed for modeling distributed networks. The new method was shown to be efficient and accurate for large-scale distributed networks. Index Terms—Distributed networks, frequency-domain data, Hamiltonian matrix, Loewner matrices (LMs), matrix format -parameters, time-domain macrotangential interpolation, model, vector fitting, vector format tangential interpolation, -parameters.

I. INTRODUCTION

I

N microwave and high-frequency applications, we are often faced with complex multiport linear structures for which it is impossible to derive accurate physics-based analytical models in the form of first-order differential equations suitable for circuit simulation. However, one can usually obtain accurate frequency-domain or -parameter data describing such structures through the use of measurement or full-wave simulation tools. In this paper, we propose a new algorithm for the automatic generation of an accurate SPICE-compatible time-domain macromodel directly from frequency-domain - or -parameter data. Several algorithms were proposed in the last few decades for macromodeling based on frequency-domain data. One approach is the global rational approximation macromodeling [1], which is based on least-squares approximations, but the application of such methods is restricted to low-order and narrow-frequency-band systems due to ill-conditioning. A moment-generation scheme based on time-domain integration was proposed in [2], but the procedures of this algorithm is numerically challenging, as pointed out in [3]. A rational Manuscript received July 06, 2012; revised September 20, 2012; accepted September 24, 2012. Date of publication November 19, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montréal, QC, Canada, June17–22, 2012. The authors are with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada H3A2A7. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222915

approximation algorithm based on Nevanlinna–Pick interpolation was presented in [4]. This method uses the mirror image of the original data points which cannot identify the original system [5]. A convex programming approach for generating guaranteed passive approximations was proposed in [6], but the method is limited to low-order systems with a smaller number of ports due to the CPU-expensive optimization process. Another approach for handling frequency-domain data is convolution-based techniques [7]–[11]. However, convolution, in general, can be computationally expensive since the convolution operator needs to take into account all of the past history [7]. Recursive convolution can be used to address this issue if a pole residue representation of the system can be found [7]. In fact, the method proposed here can be used in conjunction with recursive convolution. Recently, the Vector Fitting method [12]–[15] was developed and refined [16]–[21] as an effective method for addressing this issue. However, this method can have difficulties modeling systems with a large number of poles and a large number of ports. More recently, a new approach based on the Loewner matrix (LM) pencil has been proposed [22]–[24]. This method was shown to be very efficient and accurate compared with Vector Fitting [23], particularly for systems with a large number of ports. However, the LM approach cannot model distributed networks that are very common in microwave applications. In [25], a new LM-based approach was proposed that can handle distributed networks and is accurate and efficient for systems with a large number of ports and a large number of poles. In this paper, we expand on [25] by providing the full details of the algorithm so that it can be more easily understood and reproduced. Furthermore, a new more accurate and efficient is presented in addition to a pasway of computing and sivity checking algorithm. Finally, more detailed examples with passivity checks and comparisons with the most recent implementation of Vector Fitting [12], [18], [26] are presented. These show considerable improvement in terms of accuracy, model size, and CPU cost. In particular, an improvement of two to three orders of magnitude in accuracy was observed. II. PROBLEM FORMULATION Consider the -port linear system shown in Fig. 1. The objective of the algorithm described in this paper is to construct a SPICE-compatible time-domain macromodel based on frequency-domain multiport network parameter data, which can be obtained through measurement or simulation.

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Fig. 2. Data selection for VFTI.

Fig. 1.

-port linear network.

A. Frequency-Domain Data The system can be fully represented in the frequency domain by its -parameters (1)

Fig. 3. Data selection for MFTI.

A. Splitting the Data

where is the complex frequency, and are the vectors of port currents and port voltages, respectively, is the -parameter matrix, and is the number of ports. In many practical applications, a closed-form expression for the -parameters is not available. Instead, measured or simulated -parameters are available over a certain frequency range. This frequency-domain data is expressed as

The first step of the LM algorithm is to append the frequencydomain data with the complex conjugates at the negative frequencies, thus resulting in data points or double the original number. The data is then divided into two groups, which we refer to as the left data set and the right data set as follows:

(2)

where , , , and , , and are complex frequencies. There are a number of possible approaches for splitting the data. In this work, we have implemented two that are chosen to result in real matrices that can be easily expressed in the time domain. The first is associated with the Vector Format Tangential Interpolation (VFTI) [23] algorithm, and the second is based on the Matrix Format Tangential Interpolation (MFTI) [24] algorithm. 1) Data Splitting for VFTI [23]: In VFTI, the right data set contains the first half of the frequency points along with their complex conjugates, and the left data set contains the remaining data, as shown in Fig. 2. In other words, for the right data set, we have

where is the complex frequency, is the -parameters at frequency , and , where is the number of data points. B. Time-Domain Macromodel Our goal in this paper is to obtain a SPICE-compatible timethat matches the fredomain macromodel of the network quency-domain data in (2). This macromodel can be expressed as a linear time-invariant (LTI) system in descriptor system form with inputs and outputs as (3) where and contain the vectors of port voltages and currents, respectively, the matrices , , , and define the LTI descriptor system, and is the order of the system. is generally singular and the matrix pencil is regular. The poles . of the system are the eigenvalues of the pencil Note that a closed-form expression of the frequency domain -parameters of the system in (3) can be expressed as (4) Finally it is important to note that both and can be embedded in the system matrices as shown in Appendix A. III. LOEWNER MATRIX METHOD Here, we will present an overview of the LM method [23] for obtaining a time-domain macromodel as defined in (3) from frequency-domain data as defined in (2). This method can be summarized in the following steps.

(5) and, for the left data set, we have (6) where and denotes the complex conjugate. Note that the number of frequency samples can be assumed to be even without loss of generality. 2) Data Splitting for MFTI [24]: In the case of MFTI, the odd frequency samples along with their complex conjugates are put in the right data set and the even ones in the left data, set as shown in Fig. 3. In other words, for the right data set, we have (7) and, for the left data set, we have (8) where

.

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B. LMs

C. Real LMs

The next step of the LM algorithm is to construct the LM , the shifted LM as well as two other matrices and . This is done block by block as follows:

The LMs as constructed in (9) and (11) are complex. In order to obtain a real macromodel, real LMs can be computed using a similarity transformation [23]

(9) where , resent the th block entry of and are defined as

, and , repand , respectively, and

(10) where and are the tangential direction matrices for the right and left data sets, respectively. Then, the are constructed as follows: matrices and

(11) and as well as the number of Note that the choice of columns/rows depends on the type of tangential interpolation used. 1) Tangential Directions for VFTI [23]: and are vec. The directions are defined as follows: tors in VFTI i.e.

(12) and where , the identity matrix of size . In other words, versa. For example, the columns of given as follows:

is the th column of if , else , , and vice for and is

Note that this choice of tangential interpolation effectively means that, at each frequency point, only one row/column of the -parameter matrix is used. The rest of the data is discarded. Furthermore, in VFTI, and defined in (9) is . are scalars and the size of and and 2) Tangential Directions for MFTI [24]: For MFTI, are of size , i.e., . The directions are defined as follows:

(14) where

is a block-diagonal matrix with each block

where is the identity matrix. For VFTI, will simply be replaced by 1. On the other hand, MFTI.

, so for

D. Time-Domain Macromodel The third and final step of the LM algorithm is to extract the time-domain macromodel from the LMs. 1) Extraction of the Macromodel: A direct relationship between the LMs and the underlying time-domain macromodel was shown. In fact, it can be shown that the macromodel can be obtained by extracting the regular part of the matrix pencil [22]. The regular part can be extracted, for example, by a singular value decomposition (SVD) [22], [23] as (15) , , is a diwhere agonal matrix containing the singular values, and are the orthonormal matrices, and denotes the complex conjugate , will result in transpose. Any value of , the same SVD, except for the case where is one of the eigenvalues [23]. If a sufficient number of data points is used, the in general is not full-rank. The regular part matrix of the system is obtained by taking the first columns of and to form the following orthonormal bases:

(16) where and represent the th column of and , respectively, and is the order of the system. Then, the time-domain macromodel is extracted as follows:

(13) where and is the identity matrix. Note that the choice of interpolation results in and , and thus the whole -parameter matrix is used at each frequency point. In this case, and are and the size of and is . block matrices of size

(17) Note that the matrix is always zero at this stage, and its contribution is embedded inside the other matrices.

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Fig. 4. Normalized singular value plot.

2) Order of the Macromodel and the Impact of : Note that the order of the system is needed in (16). is determined from the plot of the normalized singular values of in (15). A large drop in the plot indicates that the underlying time-domain macromodel exists. In that case, there will be a clear separation between the singular values corresponding to the singular part and the regular part is the index of the largest drop in the plot. [27]. The order For example, the largest drop for the system shown in Fig. 4 for that system. occurs at 287, so Note that, if is present, another smaller drop in the singular , where is the number of ports. In this values occur at case, must be extracted in order to maintain the stability and passivity of the model [23].

Fig. 5. (a) Frequency-domain data covering the whole bandwidth. (b) System identification based on drops in the singular values.

IV. PROPOSED APPROACH FOR MODELING DISTRIBUTED NETWORKS The LM method was shown to be very efficient and accurate for modeling systems with a large number of ports [23]. One of the key properties of this method is that it is a system identification technique that identifies the exact order of the underlying system and extracts its actual poles. In order to achieve this, the frequency-domain data must cover most of the bandwidth of the system. For example, as shown in Fig. 5, the frequency-domain data spans the full bandwidth of the underlying lumped system and the resulting singular value plot clearly identifies the order of the system. This approach is impossible to apply to distributed networks which are common in microwave applications, because these networks have infinite bandwidth and an infinite number of poles (an example is shown in Fig. 6). In this case, it is impossible to completely identify the underlying system using a finite-order time-domain representation. In fact, for distributed systems, any extracted macromodel is a form of discretized approximation. In this paper, we present a technique based on the LM method, which generates an accurate time-domain lumped model of a distributed network from frequency-domain data over a desired bandwidth. The details of the method are given as follows. A. LMs The real LMs are constructed using the standard LM method in Sections III-A–III-C. Both VFTI and MFTI are possible.

Fig. 6. Example of a distributed system.

B. Determining the Order of the System The next step is to determine an appropriate order for the macromodel. For this, a singular value decomposition is as described in performed on the LM pencil Section III-D1 and shown as follows: (18) The normalized singular values are then plotted as shown in Fig. 7. Note that, in this case, the plot does not contain clear drops identifying the order of the underlying system as was the case in Fig. 5. This is expected as the underlying system has an infinite order. Instead our goal here is to select the order that provides the most accurate nonsingular macromodel. If the number of frequency points used is sufficient, the normalized singular values reach the accuracy threshold of the finite precision computation engine, at which point a slope change can be observed, of the macromodel is chosen as shown in Fig. 7. The order at the point of this slope change which separates the regular part from the singular part of the matrices.

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Fig. 8. Poles of the macromodel with

Fig. 7. (a) Frequency-domain data from 0 to 4 GHz for a distributed system. (b) Singular value plot.

and

embedded.

Fig. 9. Pole diagram indicating the separation of the poles.

has been determined, the regular part of the As the order LMs is extracted in the same way as shown in (16) and (17) and given as

must be extracted in order to preserve the stability and accuracy and of the macromodel. The algorithm for extracting from the system matrices is outlined here and can be divided into two main steps. The first step is to decouple the macromodel in (21) into two systems such that

(19)

(22)

C. Extraction of the Regular Part of the LMs

is the desired system and the where the system system contains the undesired poles that . The second step is are the artifact of embedding of and to compute and such that (23) (20)

which leads us to the final macromodel

resulting in the macromodel (24) (21) Note that the matrices and are zero at this stage, and their contribution is embedded inside the other matrices. D. Extraction of

and

The macromodel extracted in (21) matches the original data very accurately. However, it generally has unstable poles far from the origin, as shown in the example in Fig. 8. A similar problem was observed in the original LM method [23], where only real unstable poles were observed. This was due to the matrix in the system equations and was embedding of the corrected by extracting . In the case of distributed networks, where both real and complex poles are present, both and

with the closed-form expression defined by (25) 1) Extraction of the Model With the Desired Poles: First, the poles of the system in (21) are computed by finding the general. We then idenized eigenvalues of the matrix pencil tify the very large poles that are separated by a clear gap from the rest of the poles. Note that some of these poles may be stable. An example is provided in Figs. 8 and 9, which show a typical pole distribution (Fig. 9 is a zoomed-out version of Fig. 8). An example of the desired system poles is shown in Fig. 10. Once we have identified the desired and undesired poles, the next step is to partition the system as shown in (22).

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Fig. 10. System poles with

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and

extracted. Fig. 11. Change of error with

One way to partition is to transform the macromodel to a block-diagonal one based on the two sets of poles [28]. The process could be expensive for large-scale systems due to the generalized Sylvester equation that has to be solved to derive the block-diagonal structure. Another convenient way is Petrov– Galerkin projection which uses oblique projection of the system to find a reduced-order model [29], [30]. We employed the projection method using the left and right eigenvectors as projectors [29] to find the reduced macromodel based on the desired poles. The right and left eigenvector matrices corresponding to the system in (21) can be calculated from the following relations:

.

The macomodel is stable but does not include the . contribution of and The macomodel based on the undesired poles is formed following the same procedure mentioned in (26)–(29) as

(30) (26) where and are the diagonal matrices with the generalized eigenvalues and and are the corresponding right and left eigenvector matrices, respectively. The subspaces and to extract the desired system are then formed by preserving the eigenvectors corresponding to the desired poles as (27)

where and are the orthonormal bases of the real subspaces spanning the subspaces formed by the eigenvectors corresponding to the undesired poles. and : The next step is to compute 2) Compute and . In order to do that, the error matrices over values of equally spaced and spanning the relevant bandwidth are formed using the model extracted based on the undesired poles as follows:

where, are the indices of the desired poles. The eigenvectors are in general complex. The real subspaces are formed by splitting the real and the imaginary parts into separate vectors:

where and designate the real and the imaginary parts, and represent the real subspaces of respectively, and and , respectively. QR decomposition is then used to obtain the orthonormal bases and such that

(31) where and and are the real and complex part of the error matrix, respectively. The change of relative error with is shown in Fig. 11. As can be seen, data points is more than sufficient in most cases. is calculated by taking the average of the real part to yield

(32)

(28) The Macromodel corresponding to the desired poles is formed by an oblique projection using the orthonormal bases and as projectors

(29)

For each entry of we have equations which can be solved by the least-square approach. The following vectors are formed to apply that approach:

.. .

.. .

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Fig. 13. Circuit diagram for Example 1.

Fig. 12. Summary of the proposed algorithm.

and, finally, each entry of

is calculated as follows: (33)

where and . which is Now we have a macromodel stable and accurate and includes and explicitly outside. A summary of the proposed algorithm is provided in Fig. 12. E. Passivity of the Resulting System The passivity of the resulting system is checked by first veriis positive definite and then using the generalized fying that Hamiltonian theorem [31]. The matrices and are formed as follows:

where is a Hamiltonian and is a symplectic matrix. The system is passive if the matrix pencil has no imaginary ) eigenvalue. The LM method usually pre(real part serves passivity of the underlying macromodel [23]. We were not able to find a problem for which the model violates the passivity. However, any passivity violation can be corrected using the Hamiltonian Matrix perturbation [32], if required. V. SIMULATION RESULTS A. Example Circuits Here, we show a number of numerical examples that demonstrate the accuracy and efficiency of the proposed method. Example 1 is an 18 port transmission line network (Fig. 13) containing nine coupled lines and nine noncoupled lines. Models for both coupled and noncoupled lines are shown in [33]. The

parameter values for the coupled line are taken from [34]. The parameter values (per unit length) for noncoupled line are 3.74 , 0 S, 283.7 nH, and 84.6 pF. The length of the coupled and non-coupled lines are 0.1 and 0.05 m, respectively. Example 2 is a 36-port transmission line network (Fig. 14). This example network is formed by connecting two networks of Example 1 in parallel using a 500- resistor between each pair of similar ports. Example 3 is a 72-port network formed by connecting two networks of Example 2 in parallel using the same resistor value as Example 2 between the similar pair of ports. Example 4, shown in Fig. 15, is a 63-port network. The network contains 9 9 noncoupled lines and 6 9 coupled lines. The summary of the example circuits is provided in Table I. for Example 4 is shown in Fig. 16 to show the complexity of the problem. The frequency-domain data from 0 to 4 GHz was generated using the matrix exponential stamp [35], which relies on the solution of the telegrapher equations in the frequency domain. B. Accuracy and Efficiency Check We implemented two variations of the proposed method: MFTI and VFTI. The proposed algorithms were implemented on an Intel Core i7-2600 CPU (at 3.40 GHz) using MATLAB. The simulation results are summarized in Tables II and III. A sufficient number of frequency-domain data was used for all of the examples to identify the underlying systems. The number of data for each example was adjusted to keep the size of the same for both VFTI and MFTI. The proposed method is compared with the recent implementation of Vector Fitting. MATLAB source code of VFIT3, an implementation of Fast Relaxed Vector Fitting (FRVF), was used as the VF implementation [12], [18], [26]. The accuracy of the model was measured by the relative error (Appendix B) using 10 000 data points. The Frobenius norm of the errors (Appendix B) for these 10 000 data points for the models of the example circuits are provided in Figs. 17–20, respectively. In summary, two possible implementations of the proposed approach (MFTI and VFTI) were compared with Vector Fitting. In general, MFTI performs better than VFTI in terms of accuracy and CPU cost. Furthermore, both approaches show

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Fig. 14. Circuit diagram for Example 2.

considerable improvement over Vector Fitting and scale very well as the number of ports increases. An improvement in accuracy of two to three orders of magnitude over Vector Fitting was observed. Note that the examples presented here do not include noisy data. However, the results in [24] and [36] would suggest that the data splitting scheme of MFTI is suitable for noisy data. C. Time-Domain Simulation

Fig. 15. Circuit diagram for Example 4.

TABLE I SUMMARY OF THE EXAMPLES CIRCUITS

Transient simulations are presented in Figs. 21 and 22 in order to show the accuracy and stability of the proposed methods in the time domain. The first simulation in Fig. 21 is based on the model for Example 1, and the input at the near end was a 1-V, 2-ns pulse with 0.2-ns rise/fall time. The second simulation in Fig. 22 is based on the model for Example 4, and the input at the near end is a 1-V, 8-ns pulse with a rise/fall time of 0.2 ns. The simulations of the proposed model were done by generating a SPICE netlist of the MFTI model and simulating it in NGSPICE [37]. In order to verify the accuracy of the results, a comparison is shown with a time-domain simulation that we obtained by simple brute-force segmentation of the transmission lines. As can be seen from the simulation results, the proposed technique can be used to model systems with a considerable amount of delay as compared with the rise/fall time of the signals. D. Passivity Check

Fig. 16.

for example 4.

The eigenvalues of the Hamiltonian and the symplectic matrix pencil for all the examples are shown in Figs. 23–26, respectively (‘ ’ for MFTI and ‘ ’ for VFTI). It is evident from all of the figures that there is no purely imaginary (or very close to imaginary axis) eigenvalues for any of the examples, and we also found positive definite for all of the examples. Thus, the macromodels extracted for all of the examples are passive according to the passivity theorem mentioned in Section IV-E. Furthermore, a brute-force passivity check was performed on the macromodels for all of the examples. -parameter matrices were computed using (4) for 20 000 frequency points from 0 to 4 GHz and 15 000 points from 4 to 20 GHz; the

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TABLE II SIMULATION RESULTS (EXAMPLES 1 AND 2)

TABLE III SIMULATION RESULTS (EXAMPLES 3 AND 4)

Fig. 17. Frobenius norm of the errors for Example 1.

Fig. 20. Frobenius norm of the errors for Example 4.

Fig. 18. Frobenius norm of the errors for Example 2.

Fig. 21. Time-domain simulation for Example 1.

Fig. 19. Frobenius norm of the errors for Example 3. Fig. 22. Time-domain simulation for Example 4.

minimum value of the eigenvalues of are then plotted. The plots are presented in Figs. 27–30, respectively. The

minimum eigenvalues are always positive and constant at high frequency. Thus, all of the macromodels are passive in the

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Fig. 23. Eigenvalues of Hamiltonian matrix pencil for Example 1.

Fig. 24. Eigenvalues of Hamiltonian matrix pencil for Example 3.

Fig. 25. Eigenvalues of Hamiltonian matrix pencil for Example 2.

Fig. 27. Minimum eigenvalues of

matrix for Example 1.

Fig. 28. Minimum eigenvalues of

matrix for Example 2.

Fig. 29. Minimum eigenvalues of

matrix for Example 3.

Fig. 30. Minimum eigenvalues of

matrix for Example 4.

Fig. 26. Eigenvalues of Hamiltonian matrix pencil for Example 4.

VI. CONCLUSION range of frequency of interest as well as out of that band while we employed two different methods for checking passivity. In general, the Hamiltonian matrix-based method is sufficient and recommended.

In this paper, a new LM-based method was proposed for the modeling of systems based on measured/simulated parameters. The new approach is suitable for distributed interconnect networks which have a very high bandwidth. The new method was

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shown to be accurate and efficient compared with established techniques such as Vector Fitting, in particular for systems with a large number of ports. An improvement in accuracy of two to three orders of magnitude improvement was observed.

calculated one [using (4)]. The normalized the error is as follows:

-norm of the

(34) INCLUSION OF

AND

APPENDIX A INSIDE THE SYSTEM MATRICES

If are the system matrices, can be incorporated inside the other matrices

and

where is the squared Frobenius norm or the Hilbert–Schmidt norm of the matrix. ACKNOWLEDGMENT The authors would like to thank Dr. S. Lefteriu for her valuable information which helped give a better understanding of the original method and for providing one of the original codes to extract . The authors would also like to thank Prof. R Achar for his valuable advice to improve the paper. REFERENCES

Proof: The

-parameters of the original system are given

by

The

-parameters of the reduced system are given by

APPENDIX B ERROR CALCULATION To evaluate the overall performance of the resulting model, -norm of the error [23], [38] is used which measures the error in the magnitude of all of the entries. The same values of are and the used to find the measured/simulated -parameter,

[1] M. Elzinga, K. Virga, and J. Prince, “Improved global rational approximation macromodeling algorithm for networks characterized by frequency-sampled data,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 9, pp. 1461–1468, Sep. 2000. [2] R. Achar and M. Nakhla, “Efficient transient simulation of embedded subnetworks characterized by -parameters in the presence of nonlinear elements,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2356–2363, Dec. 1998. [3] T. Palenius, “Efficient time-domain simulation of interconnects characterized by large RLC circuits or tabulated s parameters,” Ph.D. dissertation, Dept. Electr. and Commun. Eng., Helsinki Univer. of Technol., Espoo, Finland, Nov. 2004. [4] C. Coelho, J. Phillips, and L. Silveira, “Passive constrained rational approximation algorithm using nevanlinna-pick interpolation,” in Proc. Conf. Design, Automat. Test Europe, Paris, France, Mar. 2002, pp. 923–930. [5] A. C. Antoulas, “On the construction of passive models from frequency response data,” Automatisierungstechnik, vol. 56, pp. 447–452, Aug. 2008. [6] C. Coelho, J. Phillips, and L. Silveira, “A convex programming approach for generating guaranteed passive approximations to tabulated frequency-data,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 23, no. 2, pp. 293–301, Feb. 2004. [7] A. Djordjevic, T. Sarkar, and R. Harrington, “Analysis of lossy transmission lines with arbitrary nonlinear terminal networks,” IEEE Trans. Microw. Theory Tech., vol. MTT-34, no. 6, pp. 660–666, Jun. 1986. [8] J. Griffith and M. Nakhla, “Time-domain analysis of lossy coupled transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 10, pp. 1480–1487, Oct. 1990. [9] S. Lin and E. Kuh, “Transient simulation of lossy interconnects based on the recursive convolution formulation,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 39, no. 11, pp. 879–892, Nov. 1992. [10] V. Rizzoli, A. Costanzo, F. Mastri, and A. Neri, “A general spice model for arbitrary linear dispersive multiport components described by frequency-domain data,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, vol. 1, pp. 9–12. [11] T. Brazil, “Nonlinear, transient simulation of distributed rf circuits using discrete-time convolution,” in Proc. IEEE Int. Symp. Circuits, May 2007, pp. 505–508. [12] B. Gustavsen and A. Semlyen, “Rational approximation of frequency domain responses by vector fitting,” IEEE Trans. Power Del., vol. 14, no. 3, pp. 1052–1061, Jul. 1999. [13] B. Gustavsen and A. Semlyen, “A robust approach for system identification in the frequency domain,” IEEE Trans. Power Del., vol. 19, no. 3, pp. 1167–1173, Jul. 2004. [14] D. Deschrijver and T. Dhaene, “Passivity-based sample selection and adaptive vector fitting algorithm for pole-residue modeling of sparse frequency-domain data,” in Proc. IEEE Int. Behavioral Modeling Simul. Conf., Oct. 2004, pp. 68–73. [15] D. Saraswat, R. Achar, and M. Nakhla, “A fast algorithm and practical considerations for passive macromodeling of measured/simulated data,” IEEE Trans. Adv. Packag., vol. 27, no. 1, pp. 57–70, Feb, 2004.

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[16] D. Deschrijver and T. Dhaene, “Stability and passivity enforcement of parametric macromodels in time and frequency domain,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 11, pp. 2435–2441, Nov. 2008. [17] T. Dhaene and D. Deschrijver, “Stable parametric macromodeling using a recursive implementation of the vector fitting algorithm,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 2, pp. 59–61, Feb. 2009. [18] B. Gustavsen, “Improving the pole relocating properties of vector fitting,” IEEE Trans. Power Del., vol. 21, no. 3, pp. 1587–1592, Jul. 2006. [19] B. Nouri, R. Achar, M. Nakhla, and D. Saraswat, “z-domain orthonormal vector fitting for macromodeling high-speed modules characterized by tabulated data,” in Proc. 12th IEEE Workshop Signal Propagation on Interconnects, May 2008, pp. 1–4. [20] P. Triverio, S. Grivet-Talocia, and M. Nakhla, “An improved fitting algorithm for parametric macromodeling from tabulated data,” in Proc. 12th IEEE Workshop Signal Propagation on Interconnects, May 2008, pp. 1–4. [21] A. Chinea and S. Grivet-Talocia, “A parallel vector fitting implementation for fast macromodeling of highly complex interconnects,” in Proc. IEEE 19th Conf. Electr. Performance Electron. Packaging Syst., Oct. 2010, pp. 101–104. [22] A. J. Mayo and A. C. Antoulas, “A framework for the solution of the generalized realization problem,” Linear Algebra and its Application, vol. 425, no. 2–3, pp. 634–662, Sept. 2007. [23] S. Lefteriu and A. C. Antoulas, “A new approach to modeling multiport systems from frequency-domain data,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 29, no. 1, pp. 14–27, Jan. 2010. [24] Y. Wang, C. Lei, G. Pang, and N. Wong, “MFTI: Matrix-format tangential interpolation for modeling multi-port systems,” in Proc. IEEE/ACM Design Automation Conf., Anaheim, CA, 2010, pp. 683–686. [25] M. Kabir and R. Khazaka, “Macromodeling of interconnect networks from frequency domain data using the Loewner matrix approach,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 17–22, 2012, pp. 1–3. [26] D. Deschrijver, M. Mrozowski, T. Dhaene, and D. D. Zutter, “Macromodeling of multiport systems using a fast implementation of the vector fitting method,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 6, pp. 383–385, Jun. 2008. [27] G. W. Stewart, “Perturbation theory for the singular value decomposition,” in SVD and Signal Processing, II: Algorithms, Analysis and Applications, R. J. Vaccaro, Ed. Amsterdam, The Netherlands: Elsevier, 1990, pp. 99–109. [28] P. Benner, “Partial stabilization of descriptor systems using spectral projectors,” in Numerical Linear Algebra in Signals, Systems and Control, ser. Lecture Notes in Electrical Engineering, P. V. Dooren, S. P. Bhattacharyya, R. H. Chan, V. Olshevsky, and A. Routray, Eds. Houten, The Netherlands: Springer, 2011, vol. 80, pp. 55–76. [29] P. Kürschner, “Two-sided eigenvalue algorithms for modal approximation,” Master’s thesis, Faculty of Math., Chemnitz Univ. of Technol., Chemnitz, Jun. 2010. [30] A. Antoulas, C. Beattie, and S. Gugercin, “Interpolatory model reduction of large-scale dynamical systems,” in Efficient Modeling and Control of Large-Scale Systems, K. G. J. Mohammadpour, Ed. Berlin, Germany: Springer-Verlag, Feb. 2010. [31] Z. Zheng, C. Lei, and N. Wong, “GHM: A generalized hamiltonian method for passivity test of impedance/admittance descriptor systems,” in Proc. IEEE/ACM Computer-Aided Design Conf., San Jose, CA, Nov. 2009, pp. 767–773. [32] W. Yuanzhe, Z. Zheng, K. Cheng-Kok, G. Pang, and W. Ngai, “PEDS: Passivity enforcement for descriptor systems via hamiltonian-symplectic matrix pencil perturbation,” in Proc. IEEE/ACM Computer-Aided Design Conf., San Jose, CA, Nov. 2010, pp. 800–807. [33] C. Paul, Analysis of Multiconductor Transmission Lines. Hoboken, New Jersey: John Wiley and Sons, Inc., 2008. [34] A. C. Cangellaris and A. E. Ruehli, “Model order reduction techniques applied to electromagnetic problems,” in Proceedings IEEE Electrical Performance of Electronic Packaging (EPEPS’00), Oct. 2000, pp. 239–242.

[35] R. Achar and M. Nakhla, “Simulation of high-speed interconnects,” Proceedings of the IEEE, vol. 89, no. 5, pp. 693–728, May 2001. [36] S. Lefteriu, A. Ionita, and A. Antoulas, “Modeling systems based on noisy frequency and time domain measurements,” in Perspectives in Mathematical System Theory, Control, and Signal Processing, ser. Lecture Notes in Control and Information Sciences, J. Willems, S. Hara, Y. Ohta, and H. Fujioka, Eds. Berlin, Germany: Springer, 2010, vol. 398, pp. 365–378. [37] “Ngspice: A mixed-level/mixed-signal circuit simulator,” [Online]. Available: http://ngspice.sourceforge.net/ [38] A. C. Antoulas, Approximation of Large-Scale Dynamical Systems. Philadelphia, PA: Soc. Ind. Appl. Math., 2005, ch. 5.1.

Muhammad Kabir (S’09) received the B.Sc. degree from Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, in 2005, and the M.Sc. degree from Lakehead University, Thunder Bay, ON, Canada, in 2010. He is currently working toward the Ph.D. degree in electrical and computer engineering at McGill University, Montréal, QC, Canada. He was a full-time Research Assistant with Lakehead University, Thunder Bay, ON, Canada, from May, 2010 to July 2010 and was with Motorola Telecommunication, Bangladesh, as a System Engineer from 2005 to 2008. His research interests include modeling of high-speed interconnect systems from simulated/measured parameters, fast frequency sweep algorithms for high-speed modules, parameterization of time-domain macromodels, and extraction of delays from the macromodel. Mr. Kabir served on the 2012 International Microwave Symposium organizing committee.

Roni Khazaka (S’92–M’03–SM’07) received the B.S., M.S., and Ph.D. degrees from Carleton University, Ottawa, ON, Canada in 1995, 1998, and 2002, respectively, all in electrical engineering. In 2002, he joined the Department of Electrical and Computer Engineering, Mcgill University, Montréal, QC, Canada, where he currently is an Associate Professor. In 2009, he was a Visiting Research Fellow with the University of Shizuoka, Japan. He has authored and coauthored over 60 journal and conference papers on the simulation of high-speed interconnects and RF circuits. His current research interests include electronic design automation, numerical algorithms and techniques, and the analysis and simulation of RF ICs, high-speed interconnects, and optical networks. Prof. Khazaka was the recipient of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) 2002 Microwave Prize, The Natural Sciences and Engineering Research Council (NSERC) of Canada scholarships (at the masters and doctoral levels), Carleton University’s Senate Medal and University Medal in Engineering, the Nortel Networks scholarship, and the IBM cooperative fellowship. He has served on several IEEE committees and is currently vice chair of the IEEE Montreal section. As a student he was treasurer of the Carleton University IEEE student branch (1993–1994) and later a IEEE Region 7 (Canada) student representative on the IEEE Student Activities Committee (1995 to 1998). He was Montreal section treasurer (2005/2006), Montreal section student activities co-ordinator (2004), and founding chair of the IEEE Montreal Graduate of the Last Decade (GOLD) committee. He is a member of the technical program committee of the Signal Propagation on Interconnects Workshop since 2006 and the technical program review committee of the International Microwave Symposium since 2012. He served on the organizing committee and numerous conferences such as MWCAS, NEWCAS, ISSSE, CCECE, and the 2012 International Microwave Symposium.

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CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution Shulabh Gupta, Student Member, IEEE, Dimitrios L. Sounas, Member, IEEE, Hoang Van Nguyen, Member, IEEE, Qingfeng Zhang, Member, IEEE, and Christophe Caloz, Fellow, IEEE

Abstract—A novel dispersive delay structure (DDS) based on a composite right/left-handed (CRLH)–CRLH coupler is proposed and demonstrated by both full-wave and experimental results. The experimental prototypes are compact and shielded multilayer DDSs implemented in low-temperature co-fired ceramics technology. Compared to the conventional all-pass C-section DDS, the proposed CRLH C-section DDS exhibit a larger group-delay swing, which leads to higher resolution in analog signal processing applications, as a result of their higher coupling capability. Moreover, they feature a larger bandwidth and a smaller size. A generalized wave-interference analysis is presented to both rigorously derive the transfer functions and group-delay characteristics of C-section DDSs and provide deeper insight into their operating mechanisms in both their left- and right-handed regimes. Index Terms—Analog signal processing (ASP), composite right/left-handed (CRLH) transmission lines, C-section all-pass networks, dispersion engineering, dispersive delay structure (DDS), group-delay engineering, low-temperature co-fired ceramics (LTCC).

I. INTRODUCTION

T

HE EXPLODING demand for higher spectral efficiency and the related emergence of ultra-wideband (UWB) systems in radio has spurred a renewed interest in analog real-time components and systems beyond conventional digital signal-processing techniques [1]–[5]. Digital devices are most attractive at low frequencies due to their high flexibility, compact size, low cost, and strong reliability. However, at higher frequencies, such as millimeter-wave frequencies, digital devices suffer some fundamental issues, such as poor performance, high cost of A/D and D/A converters, and excessive power consumption. At such frequencies, analog devices and related real-time or analog signal processing (ASP) systems,

Manuscript received July 09, 2012; revised September 20, 2012; accepted September 24, 2012. Date of publication November 16, 2012; date of current version December 13, 2012. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under NSERC Grant CRDPJ 402801-10 in partnership with Research in Motion (RIM). This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. S. Gupta is with the Electrical, Computer and Energy Engineering Department of University of Colorado at Boulder, Boulder, CO 80302 USA (e-mail: [email protected]). D. L. Sounas, H. V. Nguyen, Q. Zhang, and C. Caloz are with the Department of Electrical Engineering, PolyGrames Research Center, École Polytechnique de Montréal, Montréal, QC, Canada H3T 1J4. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2224362

which manipulate broadband signals in the time domain, may be more suitable, since they offer the benefits of lower complexity and higher speed in both instrumentation and communication applications[3]. Compared to the conventional phase-shifting applications [6]–[8], which are based on constant group-delay responses, recently reported ASP applications include compressive receivers [9], [10], tunable pulse delay lines [11], and pulse-position modulators [12], making use of the frequency-dependent group-delay characteristics of the dispersive devices. The core of an ASP system is a dispersive delay structure (DDS), which is a component exhibiting a nonconstant group delay versus frequency responses [13], [14]. This dispersion property is commonly used at both optical [14] and radio [9] frequencies for ASP. Specifically, a DDS phase shifts different frequencies by different amounts, based on phase specifications and its group-delay characteristics determines the frequency resolution of the ASP system. Consider a two-tone pulse propagating through a DDS, as shown in Fig. 1. In a DDS with a small group-delay swing (or small group-delay versus frequency slope), the two frequencies are delayed by amounts that are insufficiently different to resolve them in the time domain. On the other hand, a DDS with a larger group-delay slope can sufficiently separate the two frequencies, and thus provides a sufficient frequency resolution. Thus, the frequency resolution in an ASP system is proportional to the group-delay swing of its DDS, and is the most important figure-of-merit for ASP. In a typical ASP system, a broadband pulse is reshaped in real time by a DDS. Therefore, an ASP system requires a highly dispersive, compact, and a low-loss DDS operating over a wide bandwidth to efficiently process the signals in the analog fashion. Several DDS technologies have been explored at microwaves, including surface acoustic waves (SAWs) [15], magnetostatic waves (MSWs) [16], [17], super-conducting cascaded couplers [18], [19], chirped transmission lines [4], metamaterial structures [20], and reflection-type all-pass structures [21], all exhibiting different merits and drawbacks. SAW, MSW, and superconductive technologies are not suitable for several ASP applications due to restricted maximal frequency, biasing magnet requirement, and cryogenic constraint, respectively. Chirped transmission lines and reflection-type all-pass structures require a broadband circulator with a magnetic bias. Transmission-type metamaterial structures exhibit restricted group-delay profiles. Considering these limitations of existing

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TABLE I COMPARISON OF VARIOUS DDS TECHNOLOGIES AND THEIR MODES OF OPERATION (REFLECTION/TRANSMISSION)

Fig. 1. Relationship between the group-delay swing (or slope) of a DDS and the frequency resolution in an ASP system.

Fig. 2. Principle of group-delay engineering using cascaded noncommensurate all-pass C-sections consisting of shorted coupled transmission line (TL) or waveguide (WG) structures [22]. The group-delay swing of the th C-section, , is proportional to its voltage coupling coefficient, . Low values may be realized using conventional C-sections, while high values require an alternative DDS, as the CRLH–CRLH coupler DDS proposed in this paper.

DDS technologies, a transmission-type C-section all-pass DDS based on coupled transmission lines was found an attractive choice for ASP applications, due to its simplicity, flexibility for group-delay engineering, and planar configuration [22], [23]. Moreover, such a DDS can easily be cascaded with other C-sections with different group-delay characteristics to engineer the desired group delay versus frequency response, as shown in Fig. 2. The frequency resolution of an ASP system based on a C-section DDS depends on the group-delay swing of the DDS, which, in turn, depends on the voltage-coupling coefficient and the physical length of the DDS [22]. Due to practical limitations, conventional coupled-line couplers are typically restricted to coupling levels of less than 3 dB or [25]. In order to overcome this issue, while maintaining a compact component size, a new C-section DDS based on composite right/left-handed (CRLH) transmission line was recently proposed in [26]. This CRLH C-section DDS exploits the tight coupling property of the CRLH–CRLH coupler1 [28] to provide a larger group-delay swing than conventional coupled-line couplers. Thus, C-sections with small group-delay swing (and thus, low ) can be realized using conventional C-sections, while the ones requiring 1Both CRLH–CRLH and RH-CRLH couplers provide tight couplings [27] and thus could be used in the proposed CRLH C-section DDSs. We have chosen here the CRLH–CRLH alternative.

large group-delay swing (and thus, large ) may be realized using the proposed CRLH C-section DDSs, as illustrated in Fig. 2. A brief comparison between various DDSs is presented in Table I highlighting their features, benefits, and drawbacks. In addition to [26], this paper presents: 1) an extensive waveinterference explanation of the CRLH DDS, which is an essential step for the full understanding and efficient design of the DDS; 2) an experimental demonstration of the DDS using compact and shielded multilayer LTCC implementations; and 3) a rigorous comparison between the proposed DDS and the conventional C-section DDSs. This paper is organized as follows. Section II presents the conventional and proposed CRLH C-section DDSs along with their features and benefits. Section III provides the wave-interference explanation of these DDSs, which

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Fig. 3. DDS based on a: (a) conventional coupled-line coupler and (b) CRLH–CRLH coupler.

reveals the relationship between their group-delay responses and coupling coefficients. Section IV presents the experimental prototypes of the proposed DDSs in LTCC technology along with their comparison with the conventional C-sections. Finally, conclusions are provided in Section V. II. C-SECTION DDSs A C-section DDS is a two-port network obtained by interconnecting two end ports of a coupled-line coupler (four-port network), as shown in Fig. 3. Although C-sections have been known for many years, they have been used so far essentially to realize specified magnitude responses and sometimes phase equalization in microwave filters [29]. In the context of ASP, C-sections are used specifically to realize specified phase (or group delay) responses [22], and are therefore referred to as phasers [21]. A. Conventional C-Section Fig. 3(a) shows a conventional C-section DDS, which is obtained from a conventional coupled-line coupler [22], [23]. An ideal C-section DDS has an all-pass response, i.e., , with transfer function and transmission phase (1a) and (1b) respectively. In these relations, (2) is the electrical length of the lines in the coupler, where is the phase constant and is the physical length, , , and being the angular frequency, the speed of light in vacuum and the effective refractive index of the transmission line, respectively. In the case of conventional transmission lines, is constant and is typically equal to the square root of the effective permittivity. The corresponding group-delay response is (3)

Fig. 4(a) presents the typical group-delay response of a conventional C-section DDS. The corresponding magnitude responses are plotted in Fig. 4(b). Fig. 4(c) shows the phase response of an isolated conventional transmission line indicating the frequency points corresponding to minimum and maximum group-delay locations of the associated DDS. It is seen that the group-delay maxima in a conventional C-section DDS corresponds to the frequency locations where , which also corresponds to maximum coupling between the input and coupled ports, as shown in Fig. 4(b). The DDS characteristic that determine the frequency resolution in an ASP system is the group-delay swing, as discussed in Section I. The group-delay swing in a C-section may be easily computed from (3) as (4) where the condition must be satisfied for a causal response [30]. The proportionalities to the physical length and coupling coefficient in this relation have been obtained by taking the derivative of (2) and by using the second relation of (1a) with . Thus, the group-delay swing in a conventional C-section may be enhanced by increasing either the coupling coefficient, or its physical length, or both. B. CRLH–CRLH C-Section According to Section II-A, a larger coefficient is required to enhance the group-delay swing of a C-section DDS of a given size . However, conventional coupled-line couplers are restricted to relatively low ’s due to fabrication constraints [25]. The practically achievable coupling coefficients in planar configurations typically do not exceed about 3 dB, and they require broadside coupled-line architectures for highest coupling. The DDS proposed herein relaxes this constraint by employing a CRLH–CRLH coupled-line coupler instead of a conventional coupled-line coupler, due to the tight coupling property of the CRLH–CRLH coupler, where the maximum coupling level can reach up to dB [31]. This maximum coupling occurs at the transition frequency of the isolated CRLH lines forming the CRLH–CRLH coupler [28]. A typical metal–insulator–metal (MIM) implementation of a CRLH–CRLH coupler in stripline technology [27] is shown in Fig. 5. It should be noted that although the proposed DDS and the conventional C-section DDS share the same topology (an end-connected backward-coupling four-port coupler), they have very different frequency responses due to their different electromagnetic natures. While conventional C-section is an all-pass structure, the proposed DDS behaves as an all-pass response only within the bandwidth of interest. The corresponding CRLH–CRLH C-section DDS is shown in Fig. 3(b). The typical group-delay characteristic of a CRLH C-section DDS is shown in Fig. 4(d) using full-wave results corresponding to the model of Fig. 5. The corresponding coupler response is shown in Fig. 4(e). Equations (1a)–(4) are still valid for the CRLH C-section DDS, but the refractive index, , in (2) must be replaced by the frequency-dependent refractive index of the CRLH transmission line [31]. As a consequence, the DDS response is not periodic anymore, which will result in a larger

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Fig. 4. Typical characteristics of a conventional and a CRLH–CRLH coupler and corresponding DDSs. (a) Group-delay response of a conventional C-section DDS. (b) Typical -parameters of a conventional coupled-line coupler. (c) Propagation constant of an isolated right-handed (RH) transmission line. (d) Groupdelay response of a CRLH C-section DDS. (e) -parameters of a CRLH–CRLH coupler. (f) Propagation constant of an isolated CRLH transmission line. The CRLH C-section DDS corresponds to full-wave results from FEM-HFSS in the lossless case using the model of Fig. 5. For the case of the conventional coupler, and the coupler is quarter-wavelength long at GHz. the coupling coefficient is

Fig. 5. Typical MIM implementation of a CRLH–CRLH coupler in stripline configuration. The unit cell is shown in the inset with geometrical variables.

usable bandwidth, as shall be shown in Section II-C. The maximum group-delay swing is achieved at , which corresponds to in the isolated line, as seen in Fig. 4(f). C. Resolution, Size, and Bandwidth Characteristics Let us consider a practical design example to best describe the relationships between the size, the bandwidth and the frequency resolution in the CRLH C-section DDS. We shall consider a three-cell CRLH–CRLH coupler and a five-cell CRLH–CRLH coupler, and the corresponding C-section DDSs shown in Fig. 6, and compare these DDSs with conventional C-section couplers,

also shown in Fig. 6. In this design, the specified bandwidth is of 1 GHz, extending from 4 to 5 GHz. The group-delay swing provided by the three-cell DDS is equal to that of a conventional C-section with a coupling-coefficient and a length corresponding to the 11th group-delay maximum (i.e., , where is the guided wavelength). If one needs to increase the group-delay swing of the CRLH DDS for higher ASP resolution, this may be achieved by increasing the number of unit-cells of the CRLH–CRLH coupler so as to raise its coupling coefficient [28], as shown in Fig. 6, where the structure consists now of five unit cells. To achieve the same group-delay swing using a conventional C-section DDS, either the coupling coefficient or the length can be increased according to (4). However, the coupling coefficient can be increased only up to due to fabrication constraints in a practical coupler [25]. Therefore, one has no other choice than also increasing the length , as shown in Fig. 6, which is equivalent to using a higher order group-delay peak, in this case (i.e., ). As a consequence, the previous group-delay peak penetrates into the design bandwidth; hence, compromising the specified bandwidth. This shows that in a conventional C-section DDS an increase in the group-delay swing for enhanced ASP resolution results in both an increased size and a decreased bandwidth. In contrast, in the proposed CRLH C-section DDS the enhanced group-delay swing results in a moderate increase in the size and is immune of bandwidth degradation, as is apparent in Fig. 6. Thus, the

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, which corresponds to minimum coupling between the input and coupled ports of the coupler. These unusual behaviors of the group-delay response in a CRLH C-section DDS will be now explained in terms of waveinterference phenomenology in a coupled-line coupler and corresponding DDS. A. Generalized Transfer Functions and Coupling Coefficients in a Coupler Consider an ideal coupled-line coupler, as shown in Fig. 7(a), with perfect matching and infinite isolation. The coupled-port transfer function, , can be obtained by considering the interference of locally coupled waves from infinitesimal sections of length of the coupled lines. For simplicity, we shall consider the weak coupling case, where that the signal voltage remains approximately unity, , along line 1. If (rad/m) is the per-unit-length coupling coefficient between lines 1 and 2, each locally coupled wave can be written , where is the wavenumber of the uncoupled line, taking into the account the round-trip phase shift . Summing up all the wave contributions along the coupler structure, the coupled-port transfer function is found as

(5) Alternatively, the exact coupled and through transfer functions can be obtained by even–odd-mode analysis as [25] Fig. 6. Suppression of the tradeoff between bandwidth, size, and group-delay swing using the proposed CRLH C-section DDS.

tradeoff between the size, bandwidth, and resolution is essentially suppressed. III. WAVE INTERFERENCE EXPLANATION Compared to the conventional C-section DDS, the CRLH C-section DDS exhibits some surprising and interesting characteristics that are apparent in Fig. 4, and that we shall now discuss. 1) The frequency point , corresponding to maximum coupling in a CRLH–CRLH coupler, is associated with a group-delay minimum in the CRLH C-section DDS. This is a priori surprising since in a conventional C-section DDS, maximum coupling is associated with maximum group delay. 2) In the right-handed (RH) band of the isolated CRLH transmission lines constituting the CRLH DDS, the group-delay maxima of the DDS are associated with , which corresponds to maximum coupling between the input and coupled ports of the coupler; this situation is identical to that observed in a conventional C-section. However, this coupling-delay relationship is reversed in the left-handed (LH) band of the CRLH transmission lines constituting the CRLH DDS so that the group-delay maxima of the DDS correspond to

(6) (7) where (no unit) is the port-to-port voltage coupling coefficient, also assumed to be small in the approximation of the last expression of (6). Comparing (5) with (6) yields (8) depends Thus, the sign of the overall coupling coefficient on the sign of the propagation constant : in the RH frequency range, where , and in the LH frequency range, where [28]. It may be noted from (5) or (6) that maximum coupling occurs at , where in both the LH and RH cases. The transfer functions of (6) and (7) under this condition are given by (9a) (9b) B. Series-Form Transfer Function of a C-Section As mentioned in Section II and shown in Fig. 7(b), a C-section DDS is formed by end connecting the two ends of a coupled-line coupler. The generalized transfer function of a C-sec-

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Fig. 7. Wave interference phenomenology in a coupled-line coupler and a C-section DDS. (a) Four-port coupled-line coupler. (b) -long C-sections. (c) -long C-section DDS decomposed into two

tion DDS can be formed in terms of a series involving coupled-port and through-port transfer functions, and , with end connection . The C-section all-pass transfer function in terms of may be constructed as [see Fig. 7(b)]

With the group delay being simplifies to

-long C-section DDS.

, this equation

(16) (10) where each term corresponds to the transfer function of an individual propagation path between the input and output ports. For example, the term corresponds to the signal path where the signal is re-coupled back from the second line to the first line after the end-connection before reaching the output port, as shown in Fig. 7(b). The transfer function of (10) can be rewritten as (11) where (12) and . Morewhich is a convergent series since over, considering that the C-section DDS is an all-pass structure, (10) can be written as (13) Taking the derivative on both sides of the expression with respect to yields (14)

where (17) and . Note the similarity between the delay series (17) and the scattering series (12): the latter differs from the former only by its additional factor term . Since , , and are directly proportional to each other. Therefore, it may be said that the group delay of a C-section DDS [see (16)], which includes both the and series contributions, will be essentially proportional to . Depending on , which enters into the expression through , the different wave terms in (12) can give rise to a large group delay or small group delay across the DDS. Note also that since represents an electrically very short transmission line section. Different cases are discussed below. 1) Case (CRLH Transition Regime): This case corresponds to the transition frequency of the isolated CRLH line of Fig. 4(d)–(f), where the coupling coefficient is maximum. As shown in [28, eqs. (39) and (40)], the coupled transfer function of a four-port coupler at the transition frequency is (18) (19) and are the even- and odd-mode impedances where of the CRLH–CRLH coupler, respectively. Substituting these results with into (12), we get

or

(20)

(15)

. Thus, the only contribution to which implies that the group delay comes from the first term of (11) since , resulting in a minimum group delay at .

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2) Case : This case corresponds to in Fig. 4(d)–(e). Consider the DDS model of Fig. 7(b), where the electrical length is at in the RH frequency regime. We have then following (9a), so that (12) with becomes (21) This represents a constructive interference of waves represented by the loop terms, which sum up in phase up to maximize . Therefore, in the RH regime, , corresponding to maximum coupling [see Fig. 4(d)–(e)], is associated with maximum group delay. This relationship can be easily generalized to . In contrast, in the LH regime, for at , we have following (9a) so that

Fig. 8. Loop term values computed by (12) for the typical examples of (left) and (right).

(22) This represents a destructive interference of waves represented by the loop terms, which sum up in antiphase to minimize . Therefore, in the LH regime, , corresponding to maximum coupling [see Fig. 4(d)–(e)], is associated with minimum group delay. This relationship can then easily be generalized to . 3) Case : This case corresponds to in Fig. 4(d)–(f). Consider the DDS model of Fig. 7(c), of length at . Let us divide this DDS into two equal parts, of length each. Using the exact transfer function (1a) or the series form (10) of the transfer function, one finds that the transfer function of the second half of the C-section in Fig. 7(c) reduces to 1. This may be verified by inserting in (1a). As a result, the DDS of length can be equivalently modeled as a DDS of length with an end-connected transfer function . Using this new equivalent model, in the RH case where (or ) at , we get from (12) with , (23) This represents a destructive interference of waves represented by the loop terms, which sum up in antiphase to minimize . Thus, in the RH regime, , corresponding to minimum coupling [see Fig. 4(d)–(e)], is associated with minimum group delay. This relationship can easily be generalized to . In contrast, in the LH regime, for at , we have following (9a) so that we get from (12) with , (24) This represents a constructive interference of waves represented by the loop terms, which sum up in phase to maximize . Thus, in the LH regime, , corresponding to minimum coupling [see Fig. 4(d)–(e)], is associated with maximum group delay. This relationship can easily be generalized to .

Fig. 9. Steady-state spatial distribution of the voltage envelopes on a C-section structure for the two cases of LH and RH C-section DDSs computed using the ideal circuit model. The circuit model is composed of cascaded ideal coupled, where the th coupler is shorted at one line couplers of electrical length end to form the C-section DDS.

Fig. 8 plots the evolution of the successive terms of the series in a typical C-section DDS for both the RH and LH regimes. When , the successive loops terms are adding in phase following (21), whereas they are alternating in antiphase when following (22). The situation is reversed for the case of , where the successive loop terms are alternating in antiphase in the RH case following (23), whereas they are adding in phase in the LH case following (24).

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Fig. 10. Photographs of the LTCC prototypes showing the: (a) four signal layers for the four-port coupler before assembly and (b) two signal layers for the two-part DDS formed by shorting the two ends of the coupler before assembly. The CPW feed connecting the stripline structure through a via is also shown in the inset.

The constructive and destructive interference of the successive loop terms also manifests in the spatial voltage distribution on the C-section DDS, as shown in Fig. 9. For example, standing-wave patterns form at frequencies where and due to the constructive interference of waves, following (21) and (24), associated with the RH and LH group-delay maxima, respectively. Such standing-wave patterns are absent otherwise due to the destructive interference of the successive different waves traveling along the structure. IV. EXPERIMENTAL DEMONSTRATION Based on Fig. 4(d), the frequency is selected for maximal group-delay swing of the DDS. Since CRLH structures open to space are leaky [31], a shielded (boxed) stripline architecture in a low-temperature co-fired ceramic (LTCC) multilayer MIM configuration [24], identical to the one shown in Fig. 5(a), is used here to avoid radiation loss. The MIM prototypes consists of four signal layers. Fig. 10 shows their CRLH–CRLH coupler and the CRLH C-section DDS photographs. The top and bottom layers are the ground planes, and the CRLH structure is placed on layers 2 and 3. The top and bottom ground planes are connected to the shunt stubs of layer 3 by metallized vias of 6-mil diameter for potential uniformity. The structure is excited by a coplanar waveguide (CPW) feed, as shown in the inset of Fig. 10(b), where a CPW port on top layer 1 is connected to layer 3 by a metallized via. The substrate used is Dupont 951 with and . Fig. 11 shows the probe station setup for measuring the twoand four-port -parameters of the different DDSs and coupler prototypes. Fig. 12 shows the measured results of a threeand five-cell CRLH–CRLH coupler and their corresponding DDS. An acceptable matching of dB is achieved in both cases. A reasonable agreement between the measured and the full-wave simulated results is also observed, where the discrepancy is attributed to the fabrication tolerances in

Fig. 11. Photograph of the experimental setup showing the CPW probes for measuring the -parameters of the various coupler and DDS prototypes. Input and output ports of various DDSs and four-port couplers are also shown. (The conductors here have the color of the material used, silver, whereas the color of the conductor in Fig. 10 is golden (in online version), due to liquids mixed to silver for spreading as a paste in the LTCC process. Only silver remains after co-firing.).

the LTCC prototypes. A three-cell coupler has a maximum coupling of 8.7 dB corresponding to a group-delay swing of 0.68 ns. As expected, when the length is increased to five cells, the coupling level increases, namely, to 5.7 dB with a corresponding group-delay swing increasing to 2.42 ns. The maximum insertion loss in the CRLH C-section DDS is proportional to the peak group delay since the frequencies propagating the longest time inside the structure necessarily experience the maximum loss. This leads to an amplitude imbalance in , which may be easily compensated using a resistive network, as shown in [32]. Fig. 13 compares the measured group-delay response of a five-cell CRLH C-section DDS with an ideal conventional C-section DDS with various lengths and coupling coefficients.

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Fig. 12. Measured -parameters and group-delay response for a four-port coupler and corresponding DDS with: (a) three unit cells and (b) five unit cells. The photographs of the couplers are also shown on the left.

Fig. 13. Comparison of the five-cell CRLH DDS of Fig. 12(b) with conventional C-section DDSs with respect to size, bandwidth, and voltage coupling coefficient.

Starting with a conventional C-section with size and bandwidth similar to those of the CRLH C-section DDS, a coupling coefficient of 0.97 is required to achieve the same group-delay swing as that of the CRLH DDS. However, considering that such a high level of is difficult to achieve in practice in conventional coupled-line couplers, the size of the C-section can be increased to relax the coupling coefficient in order to maintain the same group-delay swing, following (4). Consequently, as discussed in Section II, due to the tradeoff between size and bandwidth in conventional C-sections, the DDS bandwidth is reduced, as shown in Fig. 13. It may thus be concluded that for a given footprint size, the proposed CRLH C-section DDS provides a larger group-delay swing due to larger coupling coefficients along with larger bandwidth, as compared to its conventional counterpart.

As illustrated in Fig. 2, several C-sections with different group-delay responses can be cascaded to synthesize a prescribed group delay versus frequency response. In particular, CRLH C-section DDSs may be used in frequency bands where a high coupling coefficient (or a group-delay swing) is required. Fig. 14(a) shows an illustration of such a DDS, where a linear group-delay response is a realized by cascading a CRLH C-section DDS with two conventional broadside-coupled C-section DDSs. Fig. 14(b) shows the corresponding LTCC prototype and measured response. The conventional C-sections provide the group-delay contribution where small group-delay swing is required while the CRLH C-section DDS provides the required group-delay engineered response. An acceptable matching is also achieved in this case.

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Fig. 14. Group-delay engineered DDS where the CRLH C-section DDS is cascaded with conventional C-section DDSs. (a) 3-D illustration. (b) Photographs of fabricated LTCC prototype and its -parameter and group-delay response.

V. CONCLUSION A novel C-section DDS based on a CRLH–CRLH coupler has been proposed and demonstrated by both full-wave and measurement results in compact shielded multilayer prototypes implemented in LTCC technology. Compared to conventional all-pass C-section DDSs, the proposed CRLH C-section DDSs have been shown to provide larger group-delay swings, and hence, higher resolution in ASP applications, thanks to their higher coupling capability, larger bandwidth, and a smaller size. Note that these DDSs may be implemented in waveguide technology [33] and are therefore available for millimeter-wave applications. A generalized wave-interference analysis has also been provided to rigorously derive the transfer functions and group-delay characteristics of C-sections DDSs, leading to deep insight into their operating mechanisms in both the LH and RH regimes. The proposed CRLH C-section DDSs are expected to provide practical solutions to high-resolution ASP systems at both microwave and millimeter-wave regimes. ACKNOWLEDGMENT The authors would like to thank Dr. D. Dousset, École Polytechnique de Montréal, Montréal, QC, Canada, for his help in probe station measurements of the various LTCC prototypes. The LTCC prototypes were fabricated at the LACIME Laboratory, École de Technologie Supérieure de Montréal, Montréal, Montréal, QC, Canada. REFERENCES [1] M. Lewis, “SAW and optical signal processing,” in Proc. IEEE Ultrason. Symp., Rotterdam, The Netherlands, Sep. 2005, pp. 800–809. [2] E. Afshari, H. S. Bhat, and A. Hajimiri, “Ultrafast analog fourier transform using 2-D LC lattice,” IEEE Trans. Circuits Syst., vol. 55, no. 8, pp. 2332–2343, Sep. 2008. [3] S. Gupta and C. Caloz, “Analog signal processing in transmission line metamaterial structures,” Radioengineering, vol. 18, no. 2, pp. 155–167, Jun. 2009. [4] J. D. Schwartz, J. Azana, and D. V. Plant, “Experimental demonstration of real-time spectrum analysis using dispersive microstrip,” IEEE Microw. Wireless Compon. Lett, vol. 4, no. 4, pp. 215–218, Apr. 2006.

[5] M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Real-time spectrum analysis in microstrip technology,” IEEE Trans. Microw. Theory Techn., vol. 51, no. 3, pp. 705–717, Mar. 2003. [6] H. Kwon, H. Lim, and B. Kang, “Design of 6-18 GHz wideband phase shifters using radial stubs,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 3, pp. 205–207, Mar. 2007. [7] Y.-S. Dai, D.-G. Fang, and Y.-X. Guo, “A novel miniature 122 GHz 90 MMIC phase shifter with microstrip radial stubs,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 2, pp. 109–111, Feb. 2008. [8] G. Boyacioglu and S. Demir, “Wideband phase shifter design using Lange coupler and radial stubs,” in Mediterranean Microw. Symp., Aug. 2010, pp. 36–39. [9] W. D. White, “Signal translation apparatus utilizing dispersive network and the like, for panoramix reception, amplitude-controlling frequency response, signal frequency gating, frequency-time conversion, etc.,” U.S. Patent 2 954 465, Sep. 27, 1960. [10] M. Skolnik, Introduction to Radar Systems, 3rd ed. New York: McGraw-Hill, 2011. [11] S. Abielmona, S. Gupta, and C. Caloz, “Experimental demonstration and characterization of a tunable CRLH delay line system for impulse/ continuous wave,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 12, pp. 864–866, Dec. 2007. [12] H. Nguyen and C. Caloz, “CRLH delay line pulse position modulation transmitter,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 8, pp. 527–529, Aug. 2008. [13] J. D. Jackson, Classical Electrodynamics, 3rd ed. New York: Wiley, 1998. [14] G. P. Agrawal, Nonlinear Fiber Optics. New York: Academic, 2005. [15] C. Campbell, Surface Acoustic Wave Devices and Their Signal Processing Applications. New York: Academic, 1989. [16] D. D. Stancil, Theory of Magnetostatic Waves. Berlin, Germany: Springer-Verlag, 1993. [17] J. D. Adam, M. R. Daniel, P. R. Emtage, and R. W. Weinert, “MSW variable time-delay techniques,” EverySpec, RADC TR-83-139, Final Rep., 1982. [18] W. S. Ishak, “Magnetostatic wave technology: A review,” Proc. IEEE, vol. 76, no. 2, pp. 171–187, Feb. 1988. [19] M. J. Lancaster, Passive Microwave Device Applications of Hightemperature Superconductors, 1st ed. Cambridge, U.K.: Cambridge Univ. Press, 2006. [20] C. Caloz, “Metamaterial dispersion engineering concepts and applications,” Proc. IEEE, vol. 99, no. 10, pp. 1711–1719, Oct. 2011. [21] Q. Zhang, S. Gupta, and C. Caloz, “Synthesis of reflection-type phasor with arbitrary prescribed group delay,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 8, pp. 2394–2402, Aug. 2012. [22] S. Gupta, A. Parsa, E. Perret, R. V. Snyder, R. J. Wenzel, and C. Caloz, “Group delay engineered non-commensurate transmission line all-pass network for analog signal processing,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 8, pp. 2392–2407, Aug. 2010.

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[23] W. J. D. Steenaart, “The synthesis of coupled transmission line all-pass networks in cascades of 1 to ,” IEEE Trans. Microw. Theory Techn., vol. MTT-11, no. 1, pp. 23–29, Jan. 1963. [24] N. Yang, C. Caloz, H. V. Nguyen, S. Abielmona, and K. Wu, “Nonradiative CRLH boxed stripline structure with high -performances,” in Proc. Int. Electromagn. Theory Symp., Ottawa, ON, Canada, Jul. 2007, pp. 1–3. [25] R. K. Mongia, I. J. Bahl, P. Bhartia, and J. Hong, RF and Microwave Coupled-Line Circuit, 2nd ed. Norwood, MA: Artech House, 2007. [26] S. Gupta and C. Caloz, “Highly dispersive delay structure exploiting the tight coupling property of the CRLH–CRLH coupler for enhanced resolution analog signal processing,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [27] H. V. Nguyen and C. Caloz, “Generalized coupled-mode approach of metamaterial coupled-line couplers: Complete theory, explanation of phenomena and experimental demonstration,” IEEE Trans. Microwave Theory Techn., vol. 55, no. 5, pp. 1029–1039, May 2007. [28] C. Caloz, A. Sanada, and T. Itoh, “A novel composite right/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 3, pp. 980–992, Mar. 2004. [29] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Networks and Coupling Structures. New York: McGraw-Hill, 1965. [30] G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures. New York: Artech House, 1980. [31] C. Caloz and T. Itoh, Electromagnetic Metamaterials, Transmission Line Theory and Microwave Applications. Piscataway, NJ: IEEE Press, 2006. [32] S. Gupta, Y. Horii, B. Nikfal, and C. Caloz, “Amplitude equalized transmission line dispersive delay structure for analog signal processing,” in Int. Telecommun. Modern Satellite, Cable, Broadcast. Services Conf., Niš, Serbia, Oct. 2011, pp. 379–382. [33] Y. Dong and T. Itoh, “Composite right/left-handed substrate integrated waveguide and half mode substrate integrated waveguide leaky-wave structures,” IEEE Trans. Antennas Propag., vol. 59, no. 3, pp. 767–775, Dec. 2010.

Shulabh Gupta (S’09) was born on December 14, 1982, in Etah, India. He recieved the Bachelors in Technology (B.Tech.) degree in electronic engineering from the Indian School of Mines, Dhanbad, India, in 2004, the Masters of Science (M.S.) degree in telecommunications from Institut National de la Recherche Scientifique Énergie Matériaux Télécommunications Research Center (INRS-EMT), Université du Quebec, Montréal, QC, Canada, in 2006, and the Ph.D. degree in electrical engineering from the École Polytechnique of Montréal, Montréal, QC, Canada, in 2012. His M.S. thesis research concerned optical signal processing related to the propagation of light in linear and nonlinear optical fibers and fiber Bragg gratings. His Ph.D. research concerned the analog signal-processing techniques using dispersion engineered structures. From December 2009 to May 2010, he was a Visiting Research Fellow with the Tokyo Institute of Technology, Tokyo, Japan, where he was involved with the application of artificial magnetic surfaces for oversized slotted waveguide antennas. He is currently a Postdoctoral Fellow with the University of Colorado at Boulder. His current research interests are high-power UWB antennas, traveling-wave antennas, dispersion engineered structures for UWB systems and devices, nonlinear effects, and Fourier optics inspired leaky-wave structures and systems. Dr. Gupta was a recipient of the Young Scientist Award of EMTS Ottawa 2007, URSI-GA, Chicago 2008, and ISAP Jeju 2011. He was the finalist in the Most Creative and Original Measurements Setup or Procedure Contest of the 2008 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS), Atlanta, GA. He was also the recipient of the Honorable Mention Award for a paper presented at the 2007 IEEE Antennas and Propagation Society International Symposium.

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Dimitrios L. Sounas (M’11) was born in Thessaloniki, Greece, in September 1981. He received the Diploma and Ph.D. degrees in electrical and computer engineering from the Aristotle University of Thessaloniki (AUTH), Thessaloniki, Greece, in 2004 and 2009, respectively. In August 2010, he joined the École Polytechnique of Montréal, Montréal, QC, Canada, as a Post-Doctoral Fellow. His research interests include analytical and numerical techniques in electromagnetics, metamaterials, and graphene-based structures.

Hoang Van Nguyen (S’01–M’09) received the B.A.Sc. degree (with honors) from the University of Toronto, Toronto, ON, Canada, in 2001, the M.A.Sc. degree from Carleton University, Ottawa, ON, Canada, in 2004, and the Ph.D. degree from the École Polytechnique of Montréal, Montréal, QC, Canada, in 2010, all in electrical engineering. He is currently a Research Associate with the Poly-Grames Research Center, École Polytechnique de Montréal, where he develops microwave circuits, antennas and systems. Dr. Nguyen was the recipient of the URSI Canadian Young Scientist Award for the Best Paper Award presented at the 2007 International Symposium on Signals, Systems and Electronics and Honorable Mention Award for a paper presented at the 2008 IEEE Antennas and Propagation Society International Symposium.

Qingfeng Zhang (S’07–M’11) was born in December 1984, in Changzhou, China. He received the B.E. degree in electrical engineering from the University of Science and Technology of China (USTC), Hefei, China, in 2007, and is currently working toward the Ph.D. degree in electrical and electronic engineering at the Nanyang Technology University, Singapore. His Ph.D. thesis is focused on dimensional synthesis of wideband waveguide filters without global optimization. Since April 2011, he was a Postdoctoral Fellow with the Poly-Grames Microwave Research Center, École Polytechnique de Montréal, Montréal, QC, Canada. His current research interests include filter synthesis, DDSs, ASP systems, and leaky-wave antennas. Mr. Zhang was the recipient of a Nanyang Technology University scholarship.

Christophe Caloz (S’00–A’00–M’03–SM’06–F’10) received the Diplôme d’Ingénieur en Électricité and Ph.D. degree from the École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, in 1995 and 2000, respectively. From 2001 to 2004, he was a Postdoctoral Research Engineer with the Microwave Electronics Laboratory, University of California at Los Angeles (UCLA). In June 2004, he joined the École Polytechnique de Montréal, Montréal, QC, Canada, where he is currently a Full Professor, a member of the Poly-Grames Microwave Research Center, and the Holder of a Canada Research Chair (CRC). He has authored or coauthored over 450 technical conference, letter and journal papers, and 12 books and book chapters. He holds several patents. His research has generated approximately 10 000 citations. His research interests include all fields of theoretical, computational, and technological electromagnetics engineering with strong emphasis on emergent and multidisciplinary topics, including particularly nanoelectromagnetics. Dr. Caloz is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Technical Committees MTT-15 (Microwave Field Theory) and MTT-25 (RF Nanotechnology). He is a speaker of the MTT-15 Speaker Bureau, the chair of the Commission D (Electronics and Photonics) of the Canadian Union de Radio Science Internationale (URSI), and an IEEE MTT-S representative of the IEEE Nanotechnology Council (NTC). He has been the recipient of several awards, including the UCLA Chancellors Award for Post-Doctoral Research in 2004, the IEEE MTT-S Outstanding Young Engineer Award in 2007, and many Best Paper Awards with his students.

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Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines Jim S. Sun, Student Member, IEEE, Humberto Lobato-Morales, Student Member, IEEE, Jun H. Choi, Student Member, IEEE, Alonso Corona-Chavez, Senior Member, IEEE, and Tatsuo Itoh, Life Fellow, IEEE

strip-resonator directional filter has good Abstract—The balance between compactness and robustness against manufacturing error. However, there have been difficulties in generalizing the strip-resonator directional filter to realize multipole filtering responses. This paper presents the theory, experiments, and improvement of a new structure of strip-resonator directional filter based on a band-reject filter. This new structure allows the realization of multipole responses and theoretically does not limit the types of filter responses. A three-pole elliptic directional filter prototype is studied thoroughly to show that its performance can be predicted accurately by a conventional filter structure. We also propose a modification of the delay-line part using composite right-/left-handed transmission line to improve the isolation. An isolation level of 30 dB is shown to be achieved consistently. Index Terms—Directional filter (DF), elliptic response, multipole DF.

I. INTRODUCTION

A

S THE frequency spectrum becomes more crowded with various wireless services, high performance channel multiplexing becomes a necessity. Directional filters (DF) are promising candidates for this application and have been the focus of many research efforts [1]–[13]. Compared with other types of multiplexing structures, a DF has the unique trait of wideband matching. This permits the development of the multiplexer system to be done in a module-by-module fashion. This is particularly useful if the number of channels needed is large, where the complexity of using other types of multiplexing structures may become unmanageable [1]. There are three main kinds of DF: hybrid-coupled, travstrip-resonator type. With eling-wave loop type, and hybrid-coupled DFs, the channel filtering response can be completely determined by a bandpass filter design [1], [3]–[5]. This is a desired trait since there is a great deal of research and experience accumulated in conventional filter synthesis [14]–[16], [18]. Also, the circuit construction is relatively easy, since it only requires 90 hybrids and bandpass filters, which Manuscript received June 30, 2012; revised September 26, 2012; accepted September 28, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with the Department of Electrical Engineering, University of California, Los Angeles, CA 90024 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.uthor, Digital Object Identifier 10.1109/TMTT.2012.2223711

are widely used and studied. However, the drawbacks are its bulkiness and bandwidth limitation. The structure requires a pair of 90 hybrids and a pair of bandpass filters. The increased size and weight may be a problem in a payload-limited platform. Also, the operational bandwidth of the whole multiplexing system is limited by the bandwidth of the 90 hybrids. In [5], an operational fractional bandwidth (FBW) is recorded to be about 50% with a three stage branch-line coupler. Wider bandwidth is achievable, but with the price of additional weight and size of increased stages. Traveling-wave loop type DFs have also been studied extensively [6]–[9]. Its structure is a lot more compact than the hybrid-coupled type. Also, multistage filtering response has been demonstrated using this structure [6]–[9]. However, unlike the hybrid-coupled directional filter, the traveling-wave loop resonator in this structure is not easy to construct. It is very sensitive to any defect in the manufacturing process. Thus, elaborate tuning effort is usually required [14]. strip-resonator-type DF strikes a balance between The the compactness and the robustness to manufacturing defects. It does not require 90 hybrid circuits, so it can be more compact than the hybrid-coupled DF. Also, its operational bandwidth can be considerably wider than the hybrid circuits. As will be demonstrated in this paper, an impedance bandwidth of more than 130% can be readily achieved. Compared with a traveling-wave-loop-type structure, it is not as compact but it does not suffer from the ultrahigh sensitivity to manufacturing defects. However, until recent years, realizing a multipole DF response with this structure has not been demonstrated [14]. Realizing a multistage DF response with this structure is the recent research focus. In [10]–[12], the idea of cascading two identical one-pole DFs for a two-stage Butterworth response is experimented and theoretically analyzed. Upon the foundation of these studies, an alternative structure has been proposed in [13]. In this new band-reject filter (BRF)-based structure, two identical BRFs are cascaded to form a DF. A three-pole elliptic DF prototype is presented in [13], demonstrating the extension of the DF response to more than two-stage and response other than Butterworth or Chebyshev. However, the work in [13] is an experimental work. No theory is provided, nor is detailed analysis of the DF performance presented. Also, the deviation of the BRF response realized in the work from the ideal elliptic response is noticeable. This paper is an extension to the work in [13]. A complete theoretical analysis of this BRF-based structure is presented, and different aspects of the DF performance are examined. We

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Fig. 1. Basic structure of the BRF-based directional filter.

confirm that there exists a theoretical bound for the rejection level in the filtering response of the DF, and it completely depends on the design of the BRF. Also, there are extra transmission zeros additional to the ones in the BRF response, of which the location can be predicted using the theory presented in this paper. The aforementioned characteristics are validated experimentally by a three-pole elliptic prototype using a new BRF modified from the one in [13]. This new BRF demonstrates a good elliptic response. Excellent correspondence among DF performance, BRF performance, and the theory is confirmed. In addition to the theoretical study, an improved version of this DF structure is proposed. One potential problem of this BRF-based structure is its isolation level at frequencies other than the center frequency. For the prototypes in [13] and in this paper, this isolation level is around 18 dB. We identify the cause of this low level of isolation and rectify the problem utilizing composite right-/left-handed (CRLH) transmission lines (TL). A new DF prototype using this CRLH technique with the same BRF is fabricated to show the effectiveness of this novel idea. Another two-pole Chebyshev DF prototype is also presented to demonstrate the capability of this BRF-based structure to realize different filter responses and different numbers of stages. This prototype also demonstrates that the BRF-based structure with the CRLH technique is able to improve the isolation in a specific frequency range. With the two CRLH prototypes in this paper, a wideband isolation level of 30 dB in the intended frequency range is consistently achieved.

Fig. 2. DF structure under common and differential excitations when the signal frequency is within the rejection bandwidth of the differential BRF.

P1 is excited, the common and differential modes are excited equally, and the two signals reflected back to P1 and P4 will interfere with each other. Thus, we can choose so that the signals interfere constructively at P4 and destructively at P1. In this way, there would be no input reflection, and the signal in this frequency band is directed to P4. The previous occurs when the signal frequency is within the BRF rejection bandwidth. If the signal frequency is outside of the BRF bandwidth, it can pass through the differential BRF, hence reaching P2 and P3 regardless of the mode of excitation. If the two modes are excited equally, then they will interfere constructively at P2 and destructively at P3. Thus, when the signal is out of the BRF bandwidth, it goes directly from P1 to P2 and flows into the next stage. By using the -parameters of the differential BRF block to trace the common and differential signal flows in the structure, we can relate the -parameter of the final DF with the -parameter of the differential BRF, shown as

II. BRF-BASED MULTIPOLE DIRECTIONAL FILTER STRUCTURE A. Theory The basic structure for this BRF-based DF is shown in Fig. 1. The differential BRF block is a filtering structure that behaves as a BRF when the upper and lower ports (P1 and P4 in Fig. 1) are excited differentially and as an all-pass filter when excited evenly. At the center frequency, ideally, the delay between the two differential BRFs will have 180 phase difference, so that they switch the excitation mode from common to differential, represents the deviation of the phase and vice versa. Here, difference of the two lines from 180 due to the frequency dependence of their phase responses. The working mechanism of this DF structure is illustrated below. In Fig. 2, we illustrate the situation when the signal frequency is within the rejection bandwidth of the differential BRF. When ports P1 and P4 are excited evenly, the signal will pass through the first differential BRF block since it behaves like an all-pass filter under common excitation. However, the delay lines between the two blocks have 180 phase difference around the center frequency, so the signal becomes differential when it reaches the second differential BRF, and it is reflected back to P1 and P4. When P1 and P4 are under differential excitation, the signal is reflected back to the two ports by the first differential BRF. Under normal working circumstances where only

(1a)

(1b) (1c)

(1d) is the -parameter of the final DF, where In (1), 1–4. The and are the -parameters of the differential BRF under common and differential excitation, respectively. , since the structure For simplicity, we assume that is of an all-pass nature under common-mode excitation. We can also affects the DF performance, since when it is not see that zero the mode switch is not perfect. During this derivation, the multiple reflections between the two differential BRFs are neglected since they have little contribution compared with other terms.

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Fig. 3. Elliptic differential BRF on which that the DF is going to be based.

From (1), we can see that the DF function can be achieved by proper selection of the delay . Around the center frequency, we to be zero so that the mode switch is would want to design terms will be zero and 100%. Under this condition, the the terms will be one. Thus, if we select to be an odd multiple of , would be zero and would be of the differential BRF, where repreequal to the . This accomplishes the DF functionality sents the angle of and assures that the filtering response of the final DF will reresponse of the differential BRF. semble the From (1d), we can also see that there are two sources for response. The first is the “BRF the transmission zeros in response of the transmission zero,” which comes from the BRF. The second one is the “extra transmission zero,” which is caused by the frequency dependency of the transmission line phase, and these extra transmission zeros are in addition to BRF transmission zeros. To see why there are extra transmission zeros, consider when the frequency is not far from the center is small. will be zero at frequencies frequency and is an even multiple of . This where can also give a quick estimation of the extra transmission zero frequencies around the center frequency. reThe major advantage of this DF structure is that the . This can be observed from (1d), sponse is bounded by response of the DF is of the differential BRF where the multiplied by terms of which amplitude is bounded by one. This implies that, when designing the DF to meet certain specifications, considering the design of the differential BRF to meet the specification would be a good start. This reduces the DF synthesis to conventional filter synthesis, where a lot of research and experiences have been accumulated. Also, as mentioned before, extra transmission zeros are introduced at predictable positions. This property can be included into the consideration of choosing the filter response type and number of stages for the differential BRF, which normally results in fewer for the same rejection requirement. B. Elliptic Three-Pole Differential BRF To validate the aforementioned theory, we develop a BRFbased DF prototype with three-pole elliptic response. As mentioned in the previous section, the key to the elliptic DF is to design a differential BRF with the same elliptic response. This differential BRF design with center frequency of 1.5 GHz is shown in Fig. 3. This differential BRF is modified and improved from the similar circuit presented in [13]. When the structure in Fig. 3 is under differential excitation, the symmetrical plane becomes a perfect electric conductor (PEC) plane. The resonators would present a short circuit at

their resonant frequencies, and the circuit behaves as a BRF. The prototype of this BRF, including the resonance frequency of the resonators, strength of coupling to the main TL, and the phase of each TL segments, are derived analytically by following [17]. To realize the elliptical function, the phases of the two line segments are unequal and are 103 and 79 , respectively. However, these phases are supposed to be frequency-independent in theory. To compensate for the frequency variation of the phase in reality, a Gradient optimization is run in ADS to fine tune the BRF prototype. The final result is the resonance frequencies shown in Fig. 3, and the transmission-line (TL) phases of 99 and 80 , respectively. The final electromagnetic (EM) structure shown in Fig. 3 is arrived by tuning (under differential excitation) the length of the resonators and interdigital capacitors to match the resonance frequencies and coupling strength after the Gradient optimization. When the structure is under common-mode excitation, the symmetric plane becomes a perfect magnetic conductor (PMC) plane. The circuit then behaves as a low-pass filter due to the loading presented to the main TL by the interdigital capacitances and the open-ended stubs. Although it is not an all-pass filter as discussed in Section II-A, the cutoff frequency of this low-pass filter is much higher than 1.5 GHz, as will be shown later. This differential BRF is simulated by Sonnet EM, and the differential and common-mode responses are shown in Fig. 4(a) and (b), respectively. The circuit is simulated with and thickness of 30 mil. Rogers RO3003 substrate with The simulation included material and radiation losses. We can see that, under differential excitation, it is a BRF centered at 1.5 GHz with 5.5% fractional bandwidth (FBW). Furresponse situated at thermore, there are reflection zeros in around 1.4 and 1.6 GHz, exhibiting the elliptic response with a side-lobe level of approximately 22 dB. According to the of the final DF should also theory presented in (1.d), the present these BRF transmission zeros at 1.4 and 1.6 GHz and side-lobe level lower than 22 dB. The theoretical elliptic response is also overlaid for comparison. The correlation between the theoretical and EM simulated response is obvious around the center frequency. The rejection level deviates from the theoretical response below 1 GHz and above 2 GHz because we use real transmission lines to approximate the frequency-independent phase shifts that are needed in theoretical filter prototype [17]. Notice the reflection zero at 2.5 GHz in the simulated response. It is caused by the anti-resonances of the resonators, that is, each branch behaves like an open circuit at this frequency, hence the loading to the main transmission line is minimal. From Fig. 4(b), we can observe that, when under commonmode excitation, the cutoff frequency of the low-pass structure is higher than 3 GHz. Thus, it should not interfere with the operation of the DF. C. Three-Pole Elliptic DF As mentioned in Section II-A, to construct the DF, we need to is an odd multiple of . From select such that the simulation for this differential BRF, we found that is about 244 at 1.5 GHz. Thus, the ideal for DF construction is estimated to be 26 .

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Fig. 5. Photograph of the constructed BRF-based DF using the differential BRF in Fig. 3.

Fig. 4. Response of the differential BRF in Fig. 3 under (a) differential and (b) common-mode excitations.

With this information, we can also estimate the position of response. As mentioned bethe extra transmission zeros in fore, these extra transmission zeros occur at frequencies where is an even multiple of . Around 1.5 GHz, to we can approximate the frequency variation of using a dispersionless TL model and the be (244 to be . Thus, the pair of frequency variation of extra transmission zeros closest to the center frequency can be estimated to be at 1.2 and 1.8 GHz. and This DF uses Rogers RO3003 substrate with thickness of 30 mil, and the fabricated prototype is shown in Fig. 5. The actual length of is found to be 27 by EM simulation with Sonnet EM, which is very close to the theoretical prediction. Simulated and measured performances of this DF are shown in Fig. 6. The measurements are shown in solid lines, and simulations are shown in dotted lines. We can see the measurement corresponds to the simulation very well, except for a small frequency shift of about 1.3%. The , and 0.4–0.7 dB for , insertion loss is about 1.2 dB for is about 5% The BRF transmission zeros in and the FBW of are recorded at 1.42 and 1.62 GHz in Fig. 6(a), which correlate very well with the response of the differential BRF and confirm the earlier theoretical analysis of (1.d). Also, the extra are also observed. The pair of extra transmission zeros in

Fig. 6. Measured prototype.

-parameters of the three-pole elliptic directional filter

transmission zeros that are closest to the center frequency are located at 1.1 and 1.9 GHz, which are close to the earlier prediction with deviation less than 8.5%. The deviation mainly comes . The frequencies of this transfrom the assumption of mission zero pair is about 27% away from the center frequency, and this assumption is not entirely true. However, it still serves as a good estimation of the positions of this transmission zero pair. If accurate prediction for transmission zero frequencies is in (1d) should be used. desired, then the full formula for and response of the DF. We can Fig. 6(b) shows the lower see that within a bandwidth of 130%, the structure has

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Fig. 8. Potential problem of a DF if the isolation level is not high.

Fig. 7. filtering response of the DF overlaid with in practice. BRF and the modified bound for

of the differential

than 17 dB and isolation between ports P3 and P1 better than 18 dB. Finally, it is important to examine how well the claim that the will be bounded by of the differential BRF applies in response of the practice. In Fig. 7, we show the measured of the differential BRF in DF overlaid with the simulated Fig. 4(a). We can see that, at the lower frequencies side from is truly bounded by of the BRF. the center frequency, has ripple levels However, at higher frequency ranges, the at some frequencies. This is because when dethat exceed of the differential BRF is assumed to be riving (1a)–(1d), of the realized differential BRF in zero. By observing the Fig. 4(b), we can see that, at frequencies higher than 2 GHz, the exceeds the rejection level of and becomes the level of dominant factor. By going through similar theoretical derivation , one can show that, in practice, but including the effect of should be as shown in the absolute bound of (2) This modified bound is also overlaid in Fig. 7 This observation shows that the rejection level of filtering of the differential BRF. function is also affected by the Thus, in a system where particularly high rejection is needed, . However, one must also pay close attention to the level of because of the additional transmission zero pair, the rejection will generally be better than up to the frelevel of quency of the first additional transmission zero. In this protofiltering response has better rejectype, it is shown that the does up to 1.35 . tion level than III. ISOLATION IMPROVEMENT BASED ON CRLH When observing the performance of the DF prototype in Fig. 6, one can notice that the isolation between P1 and P3 is very good around the center frequency but degrades pretty rapidly at other frequencies. Fig. 6 shows isolation levels around 18 dB at higher frequencies. This may not be a problem if all of the channels in the multiplexing system are receiving channels but might be a problem if some channels are transmitting with high power using a common antenna with the receiving channels.

Fig. 9. Photograph of the DF incorporating CRLH phase matching, and the realization of CRLH transmission line.

This situation is shown in Fig. 8, showing that the receiving signal would be interfered by a poorly isolated strong transmitting signal. Thus, here, we present a way to increase the isolation level to alleviate this problem while keeping other desirable advantages. in (1c), we found that the By observing the formulation of . Although we isolation level is directly proportional to to be zero at the center frequency, it increases as design the we move away from the center frequency because of the difference in the phase slope of the two microstrip delay lines. Thus, the isolation performance is very good at the center freis zero but becomes poorer away from the quency where center frequency. CRLH TLs have been studied extensively due to their ability to have their phase engineered [19]–[21]. In [21], the authors demonstrate the concept of matching the phase slope of a CRLH line to a microstrip line. Here, we adopt this concept to match is the phase slope of the two different delay lines, so that maintained to be small over a wider frequency range. However, here we face a restriction that is a predetermined delay for directionality performance, where in [21] it is a design freedom. The DF prototype incorporating the CRLH phase-matching scheme is shown in Fig. 9. It uses the same differential BRF in the original shown in Fig. 3. Note that, because design is too short to work with the CRLH line, the differential and BRF at the right is flipped. Since the simulated of the differential BRF has the same amplitude but 247 phase difference at center frequency, theoretically, should be chosen as 150 at 1.5 GHz instead of 27 . In EM simulation, we found this delay to be 152 , as shown in Fig. 9, which is very close to the theoretical value.

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Fig. 11. comparison between the directional filter with and without the CRLH phase matching.

Fig. 10. (a) -parameter and (b) the phase response of the CRLH transmission.

This 152 delay is realized by the microstrip line. Thus the other delay line will be designed as a CRLH transmission line with 28 phase advance at 1.5 GHz and the same phase slope as a 152 microstrip line. The realization of the CRLH line part of this DF is also shown in Fig. 9. A single unit cell of the left-hand transmission line is is realized in the middle of the structure. The series capacitor by a surface mount capacitor of 2.2 pF, and the shunt inductance of 4.7 nH plus a short is realized by a surface mount inductor section of shorted stub. The right-hand part is realized by 50microstrip lines with 32 delay. The structure is designed so that we obtain the best matching at the center frequency of 1.5 GHz with the desired phase delay and phase slope. The simulated performance of this CRLH line is shown in Fig. 10, where the amplitude of its -parameter is shown is shown in in Fig. 10(a), and the phase response of its Fig. 10(b). The desired phase response to match that of the microstrip line is also shown in Fig. 10(b) for comparison. We can see that the structure is of high-pass nature with cutoff around frequency around 1.25 GHz, and has a zero in 1.5 GHz. The phase of the structure is 30 at 1.5 GHz, and follows the desired phase response closely. The improvement of using this CRLH phase-matching scheme over the conventional case can be clearly seen in is plotted for both the Fig. 11, where the magnitude of

Fig. 12. -parameter response of the DF with CRLH phase matching, exhibiting high isolation.

conventional case and the CRLH case. For a wide frequency than range of 0.5–3 GHz, the CRLH case demonstrates less the conventional case does. The simulated and measured performance of this DF prototype using CRLH phase matching is shown in Fig. 12. The and response is shown in measured and simulated

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Fig. 13. Photograph of the two-stage DF with CRLH phase matching. Fig. 14. Magnitude of

Fig. 12(a). The measurement corresponds very well with the simulation, and the sharp elliptic filtering response is preserved. Also, the extra transmission zeros appear more frequently and are closer to the center frequency. This is due to the larger that we used in this design. Since larger at 1.5 GHz results in larger phase slope, the period of which the additional zeros appear is reduced. The matching and isolation of this DF is shown in Fig. 12(b). Only the measured responses are shown for the clarity of the figure. The structure is well matched with lower than 12 dB, and the isolation maintains a level around 30 dB for a very wide frequency range. Compared with the isolation performance of the conventional case in Fig. 6, it shows an improvement over 12 dB. In high-power applications, the insertion loss is critical. However, compared with the three-stage prototype without CRLH phase matching, the insertion loss only increased by a maximum of 0.25 dB across the frequency band of 0.5–3 GHz. Finally, we present a design of a two-stage DF with CRLH phase matching to demonstrate the difference in the DF design with different BRF structures and different numbers of poles and the ability of emphasizing isolation at different frequency ranges using this CRLH phase matching scheme. Fig. 13 shows the realized two-stage DF prototype. It is based on a two-stage Chebyshev BRF with a center frequency of 1.5 GHz. Notice that, because of the fewer stages in the BRF, is actually a lot shorter (ideally 90 . the phase delay in Thus, to achieve the proper directionality, a longer delay line is needed. This length works well with the CRLH of phase-matching scheme, unlike the three-stage prototype where the flip of the second differential BRF is required. The design of the CRLH part of this DF emphasizes isolation in the frequency range higher than the center frequency. It uses two unit cells of the left-handed section in between the microstrip lines, with series capacitors realized by surface-mount components of 3.9 pF on the two sides and 2 pF in the middle. The 5.1-nH shunt inductance needed in the CRLH structure is plot for this CRLH line is realized by shorted stubs. The shown in Fig. 14. We can see that is designed so that it is smaller than 15 in the frequency range higher than 1.5 GHz. Thus, we expect the isolation will be better in this spectrum range. This DF is fabricated on a Rogers RO4003 substrate with and thickness of 60 mil. Split-ring resonators are used

of the CRLH design in the two-stage DF prototype.

Fig. 15. Simulated and measured -parameter of the two-stage DF prototype.

and capacitively coupled to the two transmission lines by interdigital fingers. This DF is designed to have a center frequency of 1.5 GHz with 8% FBW. The simulated and measured -parameter responses of this DF are shown in Fig. 15. The and responses are shown in Fig. 15(a) overlaid with the simulated response of the differential BRF in the solid black curve. The measurement corresponds to the simulation very well. It can be clearly observed

SUN et al.: MULTISTAGE DF BASED ON BRF WITH ISOLATION IMPROVEMENT USING CRLH TRANSMISSION LINES

that the transmission zeros in around 1.3 and 1.75 GHz are the BRF transmission zeros, and those at 1.15 and 1.96 GHz are the extra transmission zero introduced by the BRF-based DF structure. It is noted that the locations of these extra zeros are very close to the extra zeros of the conventional three-stage DF prototype in Fig. 6(a), which are 1.1 and 1.9 GHz. This is beis 270 in both cases, and the location of the cause first additional zero pair is dominated by this factor. and In Fig. 15(b), we show the measured and simulated responses. The structure demonstrates wideband matching from 1.2 to 2.7 GHz. Notice that the isolation is better in the frequency range higher than in the center frequency, as was intended by the design of the CRLH line. It measured at least 30 dB in this frequency range and increases with frequency. IV. CONCLUSION In this paper, we give a detailed analysis of the multistage DF structure proposed in [13]. The filtering response resembles response of the differential BRF on which it is based. the Moreover, the structure is capable of generating extra transmisresponse at predictable locations, thus insion zeros in the creasing the rejection level in the stopband. The rejection level of is theoretically limited by the common-mode matching the differential BRF, but the three-stage prototype still demonstrates a low rejection level within a 70% FBW thanks to good and extra transmission zeros. From the multiplexer design point of view, this means that, in order for the DF to meet the channel filtering requirement, it is sufficient to design the differential BRF to meet the specifications. This reduces the DF response design to the BRF design, which has been extensively researched and experimented. One potential problem of this multistage DF structure is that the isolation level may not be sufficiently high at frequencies other than the center frequency. The original prototype demonstrates an isolation level around 18 dB. This can be rectified by applying CRLH phase matching for the delay lines connecting the two differential BRFs with a small penalty in insertion loss ( 0.25 dB). For the intended frequency range, a wideband isolation level of 30 dB can be consistently achieved, as verified by the two- and three-stage prototypes. REFERENCES [1] D. S. Levinson and R. L. Bennett, “Multiplexing with high performance directional filters,” Microw. J., pp. 99–112, June 1989. [2] S. B. Cohn and F. S. Coale, “Directional channel-separation filters,” in Proc. IRE, 1956, vol. 44, no. 8, pp. 1018–1024. [3] J.-S. Hong, M. J. Lancaster, R. B. Greed, D. Jedamzik, J.-C. Mage, and H. J. Chaloupka, “A high-temperature superconducting duplexer for cellular base-station applications,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 8, pp. 1336–1343, Aug. 2000. [4] S. H. Talisa, M. A. Janocko, D. L. Meier, C. Moskowitz, R. L. Grassel, and J. Talvacchio, “High-temperature superconducting four-channel filterbanks,” IEEE Trans. Appl. Supercond., vol. 5, no. 2, pt. 3, pp. 2079–2082, Jun. 1995. [5] T. K. Kataria, S.-P. Sun, A. Corona-Chavez, and T. Itoh, “New approach to hybrid multiplexer using composite right-left handed lines,” IEEE Microw. Wireless Compon. Lett., vol. 21, no. 11, pp. 580–582, Nov. 2011. [6] F. S. Coale, “A traveling-wave directional filter,” IRE Trans. Microw. Theory Tech., vol. 4, no. 4, pp. 256–260, 1956. [7] J. L. B. Walker, “Exact and approximate synthesis of TEM-mode transmission-type directional filters,” IEEE Trans. Microw. Theory Tech., vol. MTT-26, no. 3, pp. 186–192, Mar. 1978.

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[8] S. Uysal, “Microstrip loop directional filter,” Electron. Lett., vol. 33, no. 6, pp. 475–476, 1997. [9] Y. Cheng, W. Hong, and K. Wu, “Half mode substrate integrated waveguide (HMSIW) directional filters,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 7, pp. 504–506, Jul. 2007. [10] H. Lobato-Morales, A. Corona-Chavez, J. L. Olvera-Cervantes, and D. V. B. Murthy, “Multi-pole microstrip directional filters for multiplexing applications,” in Proc. Int. Conf. Electr. Commun. Comput., 2011, pp. 344–349. [11] H. Lobato-Morales, A. Corona-Chavez, T. Itoh, and J. L. Olvera-Cervantes, “Dual-band multi-pole directional filter for microwave multiplexing applications,” IEEE Microw. Wireless Compon. Lett., vol. 21, no. 12, pp. 643–645, Dec. 2011. [12] J. P. Kim, “Improved design of single-section and cascade planar directional filters,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 9, pp. 2206–2213, Sep. 2011. [13] J. S. Sun, H. Lobato-Morales, A. Corona-Chavez, and T. Itoh, “New approach to multi-stage directional filter based on band-reject filter design,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 17–22, 2012, pp. 1–3. [14] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures. Norwood, MA: Artech House, 1980. [15] R. J. Cameron, “General coupling matrix synthesis methods for Chebyshev filtering function,” IEEE Trans. Microw.Tech., vol. 47, no. 4, pp. 433–441, Apr. 1999. [16] S. Amari and M. Bekheit, “Physical interpretation and implications of similarity transformations in coupled resonator filter design,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 6, pp. 1139–1153, Jun. 2007. [17] J. D. Rhodes, “Waveguide bandstop elliptic function filters,” IEEE Trans. Microw. Theory Tech., vol. MTT-20, no. 11, pp. 715–718, Nov. 1972. [18] J.-S. G. Hong and M. J. Lancaster, Microwave Filters for RF/Microwave Applications. New York: Wiley, 2001. [19] C. Caloz and T. Itoh, “Novel microwave devices and structures based on the transmission line approach of meta-materials,” in IEEE MTT-S Int. Microw. Symp. Dig., 2003, pp. 195–198. [20] H. V. Nguyen and C. Caloz, “Metamaterial-based dual-band six-port front-end for direct digital QPSK transceiver,” in Proc. Electrotechnical Conf., 2006, pp. 363–366. [21] C.-J. Lee, K. M. K. H. Leong, and T. Itoh, “Metamaterial transmission line based bandstop and bandpass filter designs using broadband phase cancellation,” in IEEE MTT-S Int. Microw. Symp. Dig., 2006, pp. 935–938.

Jim S. Sun (S’08) received the B.S. degree from National Taiwan University, Taipei, Taiwan, in 2006, and the M.S. degree from the University of California, Los Angeles, in 2008, where he is currently working toward the Ph.D. degree. He has been a Graduate Student Researcher with the Microwave Electronics Laboratory, University of California, Los Angeles, since 2007, and his research activity includes conformal retro-directive array in the M.S. program and tunable filters, directional filters, composite right-/left-handed transmission lines, and antenna design in doctoral program.

Humberto Lobato-Morales (S’05) received the B.Sc. and M.Sc. degrees from Universidad de las Américas-Puebla, Puebla, México, in 2006 and 2008, respectively. He is currently working toward the Ph.D. degree in electronics engineering at Instituto Nacional de Astrofísica, Óptica y Electrónica, Puebla, México. In 2008, he joined the Emerging Microwave Technologies Group (EMT), Instituto Nacional de Astrofísica, Óptica y Electrónica, Puebla, México, as a Research Engineer. In 2011, he was a Visiting Student with the University of California, Los Angeles. His research interests include microwave filters and multiplexers, microwave metamaterials, material characterization using microwaves, and remote sensing systems.

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Jun H. Choi (S’12) received the B.S. degree from the University of California, Irvine, in 2003, the M.S. degree from the University of California, Los Angeles, in 2007, where he is currently working toward Ph.D. degree, all in electrical engineering. His research interests include phased-array systems, microwave/millimeter-wave circuit designs, and devices based on composite right-/left-handed and metamaterial structures.

Alonso Corona-Chavez (SM’09) received the B.Sc. degree in electronics engineering from the Institute Tecnologico y de Estudios Superiores de Monterrey, Mexico City, Mexico, in 1997, and the Ph.D. degree from the University of Birmingham, Birmingham, U.K., in 2001. His dissertation concerned microwave beamformers using high-temperature superconductors. From 2001 to 2004, he was a Microwave Engineer for CryoSystems Ltd. (U.K.), where he developed superconducting front-ends for the telecommunications industry. Moreover, he was an Honorary Research Fellow with the Electrical Engineering Department, University of Birmingham, Birmingham, U.K. (2001–2004). In September 2004, he joined the Large Millimeter Telescope, Instituto Nacional de Astrofísica, Óptica y Electrónica, Puebla, México, where he is currently a Professor with the Electronics Department. In April 2009, he was awarded a Fulbrigth fellowship to carry out research at the Electrical Engineering Department, University of California at Los Angeles. Dr. Corona is a senior member of the Institution of Engineering and Technology and a member of the National Systems for Researchers.

Tatsuo Itoh (S’69–M’69–SM’74–F’82–LF’06) received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign, Urbana, in 1969. After working for the University of Illinois, SRI, and the University of Kentucky, he joined the faculty at The University of Texas at Austin in 1978, where he became a Professor of electrical engineering in 1981. In September 1983, he was selected to hold the Hayden Head Centennial Professorship of Engineering at The University of Texas. In January 1991, he joined the University of California, Los Angeles, as a Professor of electrical engineering and holder of the TRW Endowed Chair in Microwave and Millimeter Wave Electronics (currently Northrop Grumman Endowed Chair). He has authored and coauthored 400 journal publications, 820 refereed conference presentations, and 48 books/book chapters in the area of microwaves, millimeter-waves, antennas and numerical electromagnetics. He has generated 73 Ph.D. students. Dr. Itoh is a member of the Institute of Electronics and Communication Engineers of Japan and Commissions B and D of USNC/URSI. He served as the editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES from 1983 to 1985. He was President of the IEEE Microwave Theory and Techniques Society (MTT-S) in 1990. He was the Editor-in-Chief of the IEEE MICROWAVE AND GUIDED WAVE LETTERS from 1991 through 1994. He was elected as an Honorary Life Member of the IEEE MTT-S in 1994. He was the Chairman of Commission D of International URSI from 1993 to 1996. He serves on advisory boards and committees of a number of organizations. He served as a Distinguished Microwave Lecturer on Microwave Applications of Metamaterial Structures of IEEE MTT-S from 2004 to 2006. He received a number of awards including IEEE Third Millennium Medal in 2000, and IEEE MTT Distinguished Educator Award in 2000. He was elected to a member of National Academy of Engineering in 2003. In 2011, he received Microwave Career Award from the IEEE MTT-S.

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Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave Jing Wu, Student Member, IEEE, Xi Yang, Student Member, IEEE, Shawn Beguhn, Jing Lou, and Nian X. Sun, Senior Member, IEEE

Abstract—A new type of nonreciprocal -band magnetic tunable bandpass filter (BPF) with ultra-wideband (UWB) isolation is presented. The BPF was designed with a 45 rotated yttrium iron garnet (YIG) slab loaded on an inverted-L-shaped microstrip transducer pair. With external in-plane magnetic fields from 1.1 to 1.9 kOe, the central frequency of the filter was tuned from 5.2 to 7.5 GHz, with an insertion loss of 1.6–3 dB and an UWB isolation of more than 20 dB, which was attributed to the nonreciprocity characteristics of the magnetostatic surface wave. In addition, the measured result demonstrated power-handling capabilities of over 30 dBm under room temperature. The proposed prototype with dual functionality of a tunable BPF and an UWB isolator will have many applications in RF front-end and other microwave circuits. Index Terms—Inverted-L-shaped transducer, linearity, magnetostatic surface wave (MSSW), power handling, tunable bandpass filter (T-BPF), tunable reconfigurable RF systems.

I. INTRODUCTION

M

ODERN ultra-wideband (UWB)or multiband communication systems, radars, and metrology systems need reconfigurable subsystems, such as tunable bandpass filters (T-BPFs) that are compact, lightweight, and power-efficient [1]. At the same time, isolators with a large bandwidth are widely used in communication systems for enhancing the isolation between the sensitive receiver and power transmitter. A new class of nonreciprocal RF devices that combines the performance of a T-BPF and an UWB isolator can lead to compact and low-cost reconfigurable RF communication systems with significantly enhanced isolation between the transmitter and receiver. The nonreciprocal propagation performance of magnetostatic surface wave (MSSW) in microwave ferrites, such as yttrium

Manuscript received July 10, 2012; revised September 22, 2012; accepted September 25, 2012. Date of publication November 16, 2012; date of current version December 13, 2012. This work was supported in part by the Office of Naval Research SBIR Award N0001411M0187, the Air Force Research Laboratory through Contract UES FA8650-090-D-5037, the MIT Lincoln Laboratory, and the United States Air Force under Contract FA8721-05-C-0002. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17-22, 2012. J. Wu, X. Yang, J. Lou, and N. X. Sun are with the Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115 USA (e-mail: [email protected]; [email protected]). S. Beguhn is with the Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115 USA, and also with the MIT Lincoln Laboratory, Lexington, MA 02421 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222661

iron garnet (YIG), provides the possibility of realizing such a nonreciprocal device [2], [3]. Planar ferrite structures with straight edges have been applied in filters utilizing the magnetostatic wave theory (MSW) [4]–[10]. Srinivasan et al. [9] reported a bandpass filter using two microstrip-line antennas, realized by exciting the MSSWs which can be tuned by electric field. Another issue for MSSW-based YIG resonator devices are the unwanted reflected waves from the straight edges, which will induce spurious resonance [11] due to the standing wave modes, formed from the forward and backward wave. Several kinds of techniques have been reported to suppress the unwanted reflection, including depositing a resistive absorbing film or attaching an additional ferrite material on to the edges of YIG films to absorb the MSW [12]–[15], using tapered YIG slab edges at an angle [16] or local low bias field at the edge of the film [14]. However, these approaches need extra effort to implement. Conventionally, YIG MSW filters have a relatively low power handling due to the narrow spin-wave linewidth of a single resonance mode [23], [26], [27]. Increasing the power-handling capability has been an open challenge for such YIG devices. In this paper, starting from the theoretical analysis and simulation of magnetostatic wave propagation in YIG slabs, a new method of suppressing the spurious resonance is proposed. The YIG slab was then rotated by a proper angle to diminish standing-wave modes, which leads to a much smoother passband, and a tunable nonreciprocal bandpass behavior. The designed -band T-BPFs filters have a central frequency shift from 5.2 to 7.5 GHz under in-plane magnetic fields from 1.1 to 1.9 kOe with a reasonable insertion loss 3 dB. The nonreciprocal transmission characteristics of the forward and backward MSSW leads to more than 20-dB isolation across all measured frequency ranges. The power-handling capability of the proposed nonreciprocal BPFs will also be discussed. The measured result demonstrated 1-dB compression point over 30 dBm under room temperature. II. THEORY AND MODELING A. MSW in Tangentially Magnetized Ferrite MSW can be excited in a YIG slab loaded on an inverted-Lshaped microstrip transducer pair [20], as shown in Fig. 1. The of the single crystal YIG slab saturation magnetization is about 1750 Gauss, and the ferromagnetic resonance (FMR)

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slab [20]. More specifically, MSSW with a

wave propagates

wave propagates on the top on the bottom surface while a surface. Magnetic potential has a maximum at the surfaces and decays inside the slab and there is only one mode exists in the ferrite, given as (3)

Fig. 1. Geometry of the proposed BPFs. (a) Inverted-L-shaped microstrip transducers with parallel YIG slab alignment. (b) Inverted-L-shaped trans0.37 mm, 0.32 mm, ducer with rotated YIG slab alignment. 1.2 mm, 2 mm, 4 mm, 3.6 mm, 2.6 mm, . and

where is the wave number along the -axis and is the thickness of the slab. Under the bias condition , magnetostatic back volume wave (MSBVW) will be excited inside the YIG slab [20]. The magnetic potential has sinusoidal distribution. The back volume wave consists of multimodes with the same cutoff frequencies given by

(4) For practical filter designs, the MSBVW will suffer from ripples due to the multiresonance modes, while MSSW usually have a better resolution due to its single resonance. B. Nonreciprocity in Ferrite Slab With Finite Size

Fig. 2. Dispersion relation of MSSW and MSBVW in infinite YIG slab, with 108 m. dc bias magnetic field 1.6 kOe, The thickness of the slab is

linewidth is less than 1 Oe at -band. Suppose the external bias magnetic field is along the -axis, the permeability of a single-crystal YIG can be approximated as a frequency-dependent tensor as

When the YIG slab is placed parallel to the transducers and the bias magnetic field , as shown in Fig. 1(a), the excited MSSW is reflected at the edges of YIG slab, bouncing back and forward. A set of discrete standing-wave modes will be formed [11] when the wave number meets (5) where and are the wave numbers for forward and backward propagation in the YIG slab, respectively, and is the distance between the two edges of the YIG slab. In addition, the finite length of the films generates additional modes (6)

(1) , , is the dc bias field, where and is the angular frequency [21]. With the magnetostatic approximation, the wave propagation in an infinite YIG slab follows the Walker’s equation (2) Supposing that the YIG slab was infinite size and ignoring in-plane boundary conditions, the dispersion relation of MSW was calculated and plot as shown in Fig. 2. Under the bias condition , MSSW will be excited at the surface of the YIG

The dispersion relation of MSSW propagating in a finite YIG slab can be expressed as [11]

for inside YIG slab for outside YIG slab

(7)

indicates where is the thickness of the substrate and the wave number of MSSW. The dispersion relation was plotted in Fig. 3. The input and output transducers can both be coupled at these discrete resonances, which leads to a reciprocal BPF. On the other hand, the passband will be split by spurious

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Fig. 3. Dispersion relation of MSSW in a finite YIG slab placed parallel to 381 m; the bias magnetic field. The thickness of transducer substrate is 108 m, and 1.6 kOe. denotes the thickness of YIG slab is standing-wave modes, and is related to the finite length. Fig. 5. Calculated radiation resistances and transduction loss to the top and bottom surfaces of the YIG slab under a bias field of 1.6 kOe.

can be modeled as an equivalent lossy transmission line [20], [22] As the incident wave propagates along the transducer, energy is lost to the MSSW excitation. The radiation resistance per unit length for surface waves traveling in the direction can be written as [27] (8) Fig. 4. Schematic of MSW propagation in a YIG slab with a 45 edge, all the directions in this figure are in-plane.

standing-wave modes and finite length modes . To diminish the splitting modes and achieve the nonreciprocity characteristics, the YIG slab was rotated by 45 , as shown in Fig. 4. Suppose the bias magnetic field is applied in-plane and perpendicular to the MSSW. After the reflection on the 45 edge, the wave will propagate parallel to the bias field, which follows the MSBVW condition. However, because it is operating in the stopband of MSBVW, the reflected wave will decay fast and the energy dissipates along this path. Therefore, the standing-wave resonances will not exist. C. MSW Excitation Experimentally, it is easy to excite the MSSW by placing a current carrying wire near a YIG slab. Most commonly, microstrip structures with short pins to the ground plane at the end of the strip line are utilized to achieve the excitation. Adam et al. [8] adopted parallel microstrip as the transducers. Most recently, a T-shaped microstrip coupling structure and YIG films were used to achieve a low-loss -band T-BPF [10]. An L-shaped microstrip transducer was reported in [6] and [7], which could enhance the coupling to a minimum insertion loss of 5 dB [7]. In order to improve the insertion loss and isolation and achieve the nonreciprocal behavior at the same time, an inverted-L-shaped transducer has been designed, as shown in Fig. 1(a). The transducer is designed on a 0.381-mm-thick Rogers TMM 10i substrate with and . Usually, the coupling between the current flowing on the microstrip transducer and the MSSW propagating in the ferrite slab

where indicates array factor for the current flowing on microstrip transducer with , is the MSSW wave number, is the width of the transducer, is the Bessel function of zeroth-order, and is the vertical spacing between the transducer and YIG/air interface. Here, it is 40 m for bottom surface of YIG and 148 m for the top surface. With an open end, the current distributes nonuniformly across the inverted-L-shaped transducer. The total radiation resistance can then be estimated as (9) where

indicates the current on the transducer, considers of the substrate, is the distance from the open end, and is the overlap length of YIG slab and transducer. Fig. 5 shows the calculated radiation resistance under a bias field of 1.6 kOe. The frequency band for MSSW is from 6.5 to 6.9 GHz. Due to the nonreciprocal field displacement, is quite different between MSSW propagating on the bottom surface and top surface . When YIG is rotated by 45 , the overlap length of the transducer reduced to 2.5 mm. At 6.7 GHz, and . Therefore, the coupling to the top surface can be neglected, while the bottom coupling dominates the MSSW propagation in the YIG slab. If we suppose the feeding transducer is ideally 50 at 6.7 GHz, the transduction loss due to impedance mismatch on the bottom surface (forward transmission) can be approximated as 0.04 dB, including the transmit and receive transducer. Here, .

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TABLE I INDEXING OF RESONANCE MODES

Fig. 6. Simulated and measured result of BPFs with YIG resonator aligned parallel to the transducer, dc magnetic bias field is 1.6 k Oe, applied perpendicular to the feed line: (a) simulated and (b) measured.

Fig. 7. Simulated and measured results of BPFs with a YIG resonator aligned 45 against the transducer.

A. Simulated and Measured Results If the YIG is aligned parallel to the transducer, the reflection from the edges generate surface wave on the top surface, which leads to reciprocal performance and splitting resonance modes. On the other hand, when rotated YIG is applied, the surface wave is limited on the bottom surface due to the nonreflection edges. Nonreciprocity and nonsplitting characteristics can be achieved. D. Propagation Loss of MSSW Filters At a given frequency, the propagation loss of MSSW can be approximated as [20] (10) where is the FMR linewidth of YIG in Oe and is the group delay in the YIG slab, defined as . The propagation loss under a bias field of 1.6 kOe was calculated as plotted in Fig. 5. 0.30 dB was observed for the single-crystal YIG with separation of transducer 1.2 mm. III. RESULT AND DISCUSSION The proposed transducers were simulated with Ansoft High Frequency Structure Simulator (HFSS) 12.1 and then fabricated and measured via a vector network analyzer (Agilent PNA E8364A). The input power for the measurement is 12 dBm.

Fig. 6 showed the simulated and measured -parameters of our BPF with the YIG resonator aligned parallel to the transducers. and responses are reciprocal, with an insertion loss 1.8 dB at the primary resonant frequency of 6.7 GHz, and the 3-dB bandwidth is 170 MHz. However, the discrete resonant modes lead to a passband with many ripples. The indexing of these resonance modes was shown in Table I. The measured results showed higher insertion loss for than the simulated results did, because of the roughness of the edges from the fabrication process. The reflection from the edges of the YIG slab was reduced in measurement compared with an ideal boundary in simulation. When the YIG resonator was rotated 45 around its center, and showed nonreciprocal transmission behavior. Also, the passband becomes much smoother due to the suppression of the reflections from the edges. The insertion loss of forward transmission is about 1.65 dB at 6.7 GHz, with a bandwidth of 220 MHz (3.2%), while the reverse transmission has isolation greater than 22 dB, as was shown in Fig. 7. B. Magnetically Tuned Resonant Frequency The BPF with 45 rotated YIG resonator was also measured from 5.3 to 7.5 GHz under a dc magnetic field of 1.1–1.9 kOe, as shown in Fig. 8. The results indicated a well-shaped BPF with insertion loss between 1.6–3.0 dB, and bandwidth around 220 MHz at 6.7 GHz. It is notable that this type of design has a relatively high of 30 compared with other ferrite T-BPFs.

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Fig. 9. Filter performance with the rotated YIG slab. (a) with YIG 500 m. (b) Comparison of 3-dB bandwidths between two thickness thicknesses.

and are also plotted in Fig. 9(c) and (d). The reflection coefficients are similar, which are less than 10 dB under most bias fields applied. This indicates that energy dissipates in the YIG film, instead of reflecting back at the ports when fed at port 2. Another possible reason for higher insertion loss at lower frequencies is the impedance mismatch. At 5.2 GHz (1.1-kOe bias), the return loss is 8.8 dB, and is 7.23 dB while both are over 25 dB at 6.7 GHz. Further optimization on the transducer design may help improve the impedance matching at any specific operating frequencies in a practical application. In addition, to achieve higher power-handling capability, the BPFs with a 500- m-thick rotated YIG slab was also presented. The measured transmission coefficient was shown in Fig. 9. The 3-dB bandwidth in this case was around 300 MHz under a 1.9-kOe bias field, compared with the bandwidth of 240 MHz when the YIG resonator had 108- m thickness. Fig. 8. -parameter measurement results of the inverted-L-shaped transducers . (b) . (c) . (d) . loaded with a rotated YIG slab. (a)

The resonant frequencies follow the Kittel’s equation [19] and can be tuned by dc magnetic fields. Furthermore, nonreciprocal performance was observed with isolation over 22 dB between two transmission directions within the filter turning range from 5 to 7.5 GHz. The rejection band is over 15 dB for 2–10 GHz.

C. Insertion Loss Analysis The total insertion loss of the BPFs pass band can be estimated as Other Loss (dB)

(11)

and can be calculated with (8)–(10), in terms of where various bias magnetic fields and central resonant frequencies, as shown in Fig. 10. and are the conduction loss and

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TABLE II IP3 dB WITH VARIED BIAS FIELDS

Fig. 10. Insertion Loss Analysis of the proposed BPFs.

Fig. 11. Experiment setup for power-handling test of the proposed nonreciprocal BPFs.

dielectric loss of the microstrip transmission line, respectively. is estimated to be 0.3034 dB, and is 0.08 dB at 6.5 GHz for our transducers fabricated on Rogers TMM 10i substrate with and total trace length 2.8 mm. Due to the small size of the YIG resonator, is around 0.2 to 0.4 dB, with a minimum at 5.2 GHz. Radiation resistance increased from 23.6 to 87.3 , when 1.1-1.6-kOe bias fields was applied. The mismatching leads to a transduction loss of 1.2 dB at 5.25 GHz and 0.67 dB at 7.5 GHz, which contributed to the major insertion loss increase, compared with 0.04 dB at 6.5 GHz. IV. POWER-HANDLING CAPABILITY High-power measurements of the BPF were then carried out to investigate the power-handling capability of the nonreciprocal BPFs. The schematic of the measurement setup is shown in Fig. 11. The preamplifier provides 30 2 dB gain in the 4–8-GHz range. A sweep of the variable network analyzer (VNA) output power between 27 to 0 dBm gave an input power for the device under test (DUT) in the range of up to 30 dBm. Our nonreciprocal BPFs were then tested with varied bias magnetic fields from 1.1 to 1.9 kOe, which tuned the resonance frequency of the BPF from 5.2 to 7.5 GHz. In order to compare the 1-dB compression point under different bias fields and investigate the maximum BPFs tuning range with high power handling, the output transmitted powers were normalized with the input power and the insertion loss of the filters at 0-dBm input power. Fig. 11(a) and (b) showed the test results of the BPFs with a rotated-YIG slab with two slab thicknesses of 108 m and 500 m, respectively. For 108 m, is 30 dBm for the lower edge of the tuning range (1.1-kOe bias at 5.2 GHz). went up to greater than 30 dBm when

the bias field was increased to 1.3 kOe. At the optimal operating region, where the lowest insertion losses were observed (1.5–1.7 kOe), is 27–28 dBm, the was reduced to 23.5 dBm at the upper edge (1.9-kOe bias at 7.5 GHz). Since the power compression level of resonators is proportional to its volume [23], for a given YIG dimension of and , better power-handling capability of the resonator was expected for the BPF with a 500- m-thick YIG slab. Table II shows a comparison between these two filters with different resonator thickness. At the optimal tuning region, the are all greater than 30 dBm for the thicker YIG slab. From Fig. 12 and Table II, one can see that the BPFs all have certain frequencies where the high power-handling capability is 30 dBm, 5.15–5.73 GHz for the BPF with 108- m YIG slab, and 6.24–6.80 GHz for the BPF with the 500- m YIG slab. At the tuning edge of the lower frequencies, the normalized output power with 1.3-kOe bias dropped slower than that with 1.1 kOe. At the upper tuning edge, the output power with 1.9-kOe cutoff has a smaller input power than that with 1.7 kOe. Therefore, for YIG resonator with both thicknesses, downgraded at both lower and upper tuning edges. It is notable that the normalized output power sometimes went above 0 dB around the 1-dB compression point. This is due to the insertion loss changes compared with those under low power. Nonetheless, the upshift is less than 1 dB and will hardly affect the overall power-handling capability. There are two major factors that cause these nonlinearity performances: coincidence-limiting effect of ferrite [24] and the premature saturation [25]. The coincidence-limiting effect is related to a subsidiary absorption from coupling between the uniform precession mode and the spin waves with half of the frequency of this mode. The absorption happens below , 4.9 GHz for YIG slabs, where the MSSW devices saturated at a low power level (typically 0 dBm). These effects contribute to the downgrade of at the lower edge of the BPFs tuning range. For our MSSW BPFs, the closer the operating frequency to , the lower power handling they can achieve. A typical solution for devices intended to operate below 4.9 GHz is to use doped YIG or other ferrites, whose saturation magnetization are smaller than 1750 Gauss. The premature saturation is related to the instability of susceptibility that arises from nonlinear terms proportional to the exchange and anisotropy energies [23]. The susceptibility first increases and then sharply drops. When the RF power increases

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Conventionally, YIG-based bandpass filters are based on its uniform resonance mode, i.e., FMR [23]. Adam et al. [27] showed a MSW filter has 0-dBm power handling with 15-MHz bandwidth at 9 GHz. Hoefer et al. [26] showed that typical MSW filters with 0.2%–0.5% bandwidth can achieve 50-mW power handling (17 dBm). The bandwidth of our filters are around 300 MHz at 6.7 GHz (4.48%), which leads to roughly 10–13 dB increase on . Although the quality factor is lower than other filters based on single resonance modes, the MSSW filter designed based on this concept can achieve a much higher power-handling capability. Self-heating will be expected during the MSSW propagation and absorption. In real applications, an additional packing technique, e.g., heat sinks, may be applied to dissipate the heat effectively. V. FILTER PARAMETER ANALYSIS

Fig. 12. Transmitted power of the proposed BPF in terms of input power, with various of bias magnetic field from 1.1 to 1.9 kOe. The output power is normalized with the input power, and the insertion loss of DUT at 0 dBm. The BPFs 108 m and (b) 500 m. with two YIG thicknesses are measured: (a)

to greater than the threshold, the critical field of this threshold power can be estimated as [25] (12) where is the FMR linewidth of YIG, is the spinwave linewidth, defined as , where the 3-dB bandwidth of the resonance with is the gyromagnetic coefficient, and is the FMR frequency related to the external bias field. Therefore, the power-handling capability of MSSW filters is proportional to the bandwidth while inversely proportional to the operating frequency or bias field. This effect contributes to the downgrade of at the upper edge of the tuning range of the BPFs. According to (12), the critical field decreased when the FMR frequencies increased, which led to a lower cutoff input power. The bandwidth for BPFs with 108- m YIG resonator is around 240 MHz while is around 300 MHz for 500- m YIG at bias field 1.9 kOe, as shown in Fig. 9(b). Therefore, higher is expected for thicker YIG slabs, which means higher power handling. A comparison of Fig. 12(a) and (b) indicates a good agreement with these analyses. The cutoff input power increased from 23 to 26 dBm for thicker YIG, with 1.9-kOe bias field.

The important design parameters and performance of the twoport nonreciprocal MSSW filter are discussed here. These parameters can be divided into geometrical, magnetic, and filter performance parameters, defined here. 1) Geometrical parameters: slab length and width , thickness , rotation angle , and overlap length of the transducer . 2) Magnetic parameters: external bias magnetic field , YIG-film saturation magnetization , FMR linewidth , and resonator spin-wave linewidth . 3) Filter performance parameters: nonreciprocity, group delay , and 3-dB bandwidth . A. Geometrical Parameters 1) Slab width : For the parallel aligned YIG case, the width will determine the resonance frequency of the standing-wave modes . Moreover, because the separation between the main resonance and the finite length modes is inversely proportional to , the interference of width modes with the main resonance can be minimized by choosing the parameter to be as small as possible. After rotating the YIG film, the standing-wave modes are eliminated, the slab width will affect the propagation loss rather than the resonant frequency. 2) Slab length : the parameter determines the wavelength of the finite-length mode resonances. From the finite-length mode dispersion relation calculations , reducing the value of will increase the frequency separation between the resonances and result in better rejection of the (1, 2) resonance with respect to the main resonance (1, 1). However, as decreases, the power-handling capability of this filter will decrease, due to the decrease of volume of the device. 3) Overlap length of the transducer : this parameter determines the coupling between transducers and the YIG slab, which affect the input and output reflection coefficients. According to (9) and Fig. 5, the optimal for our case is around 2.6 mm

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TABLE III EXPERIMENTALLY MEASURED NONRECIPROCITY IN TERMS OF ROTATION

4) Rotation angle : from the previous analysis, the rotation of YIG film will cause the nonreciprocity. Rotated by 45 is the optimal design, considering both insertion loss and the nonreciprocity. In fact, the rotation with over 15 can lead to an obvious nonreciprocity. Table III shows the experimentally measured relation between rotation angle and the nonreciprocity. The isolation ( ) is decreased from 22 to 12 dB, if we change the rotation angle from 45 to 15 . The insertion loss ( ) is increased from 1.8 to 4.1 dB. 5) Thickness : from the experimental results, a thicker YIG slab leads to wider 3-dB bandwidth. More detailed bandwidth analysis will be given in Section VI. At the same time, since the power compression level of the resonator is proportional to its volume, for a given dimension of and , the thicker the YIG is, the better the power-handling ability of the filter will be.

Fig. 13. Group delay of the nonreciprocal filter with rotated aligned YIG thick108 m, under bias magnetic field of 1.6 kOe. nesses

Fig. 14. Dispersion relation of the MSSW propagation in a YIG slab with thick108 and 500 m, under bias magnetic field from 1.1 to 1.9 kOe. nesses

B. Magnetic Parameters 1) External bias magnetic field : the orientation of the bias magnetic field determines the FMR frequency of MSSW filters, as well as the operating frequency. 2) YIG-film saturation magnetization : the orientation of the bias magnetic field determines the FMR frequency through the permeability tensor. 3) Resonator spin-wave linewidth : this parameter is defined as : is the half-power bandwidth of the resonator. The power-handling capability of MSSW filters is proportional to bandwidth, as stated in (12). C. Filter Performance Parameters 1) Nonreciprocity of the BPFs is determined by rotation angle . A 45 degree rotation angle leads to minimum insertion loss and maximum isolation. 2) Group delay : group delay is the rate of change of phase response with frequency. It can be estimated by in both HFSS simulation and VNA measurement. Also, analytically, group delay can also be derived via the dispersion relation, as , where is the length along the propagation path. The group delay of the nonreciprocal filter was analyzed with rotated aligned YIG thicknesses 108 m, under bias magnetic field 1.6 kOe. From Fig. 13, we can see a good agreement among analytical, simulated, and measured results. A flat group delay around 2.5 ns can be observed from 6.55 to 6.75 GHz, which is roughly inside the 3-dB

bandwidth of the passband. The increase of group delay at higher frequency attributes to the upper cutoff edge of the passband. 3) Bandwidth: the 3-dB bandwidth of the proposed BPF can attribute to both propagation losses (PL) and transduction losses (TL). Fig. 14 shows the dispersion relation of the MSSW propagation in a YIG slab with thicknesses 108 and 500 m, under different bias magnetic fields from 1.1 to 1.9 kOe. Thicker YIG slab leads to wider propagation band for MSSW. The passband has a good agreement with Fig. 9(b), where 220-MHz bandwidth is observed for 108 m; while 300 MHz bandwidth is observed for 500 m. However, the decrease in bandwidth with low bias field (1.1 to 1.4 kOe) might attribute to the increase of transduction loss. The radiation resistance is less than 25 at 1.1 kOe, as shown in Fig. 10. The loss due to the weak coupling limits bandwidth. From these parameter analyses, one can control the preferred specification for filter designs. VI. CONCLUSION In summary, a novel nonreciprocal -band magnetic T-BPF with a YIG slab has been designed, fabricated, and tested, which is based on an inverted-L-shaped coupling structure loaded with a rotated single-crystal YIG slab. MSSW propagation in the rotated YIG leads to nonreciprocal performance. The tunable resonant frequency of 5.2–7.5 GHz was obtained for the BPF

WU et al.: NONRECIPROCAL TUNABLE LOW-LOSS BPFs WITH UWB ISOLATION BASED ON MAGNETOSTATIC SURFACE WAVE

with a magnetic bias field of 1.1–1.9 kOe applied perpendicular to the feed line. At the same time, the BPF acts as a UWB isolator with more than 20-dB isolation at the passband with insertion loss of 1.6–3 dB. Power-handling capability of over 30 dBm has been demonstrated under room temperature in the filter’s tuning range. The demonstrated nonreciprocal magnetically T-BPFs with isolator dual functionality and with high power handling should be promising in -band RF front-end and other microwave circuits. ACKNOWLEDGMENT X. Yang and J. Wu contributed equally to this paper. The authors would like to thank Prof. Y. K. Fetisov, Moscow State Institute of Radioengineering, Russia, Prof. A. Slavin, Oakland University, and Prof. I. Zavislyak, Kiev National University, Ukraine, for enlightening discussions.

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[20] D. D. Stencil, Theory of Magnetostatic Waves. Berlin, Germany: Springer-Verlag, 1993. [21] E. Schlomann, “Microwave behavior of partially magnetized ferrites,” J. Appl. Phys., vol. 41, pp. 1350–1350, Mar. 1970. [22] P. R. Emtage, “Interaction of magnetostatic waves with a current,” J. Appl. Phys., vol. 49, pp. 4475–4475, 1978. [23] W. S. Ishak and K. W. Chang, “Tunable microwave resonators and oscillators using magnetostatic waves,” IEEE Trans. Ultrason., Ferroelectr. Frequency Control, vol. 35, no. 3, pp. 396–405, May 1988. [24] J. P. Parekh, K. W. Chang, and H. S. Tuan, “Propagation characteristics of magnetostatic waves,” IEEE Trans. Circuits Syst. Signal Process., vol. 4, no. 1-2, pp. 9–39, 1985. [25] A. J. Heeger, “Spin-wave instability and premature saturation in antiferromagnetic resonance,” Phys. Rev., vol. 131, no. 2, pp. 608–616, Jul. 1963. [26] J. Uher and W. J. R. Hoefer, “Tunable microwave and millimeter-wave band-pass filters,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 4, pp. 643–653, Apr. 1991. [27] J. D. Adam, “AN MSW tunable bandpass filter,” in Proc. IEEE Ultrason. Symp., 1985, pp. 157–162. [28] J. Wu, X. Yang, J. Lou, S. Beguhn, and N. X. Sun, “Non-reciprocal tunable low-loss bandpass filters with ultra-wideband isolation based on magnetostatic surface wave,” in Proc. Int. Microw. Symp., Montreal, QC, Canada, 2012, pp. 1–3.

REFERENCES [1] J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microstrip Applications. New York: Wiley, 2001. [2] J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann, and S. N. Stitzer, “Ferrite devices and materials,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 721–737, Mar. 2002. [3] P. W. Wong and I. C. Hunter, “Electronically reconfigurable microwave bandpass filter,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 12, pp. 3070–3079, Dec. 2009. [4] Y. Murakam and S. Itoh, “A bandpass filter using YIG film grown by LPE,” in IEEE MTT-S Int. Microw. Symp. Dig., 1985, pp. 285–287. [5] Y. Murakami, T. Ohgihara, and T. Okamoto, “A 0.5–4.0-GHz tunable bandpass filter using YIG film grown by LPE,” IEEE Trans. Microw. Theory Tech., vol. 35, no. 12, pp. 1192–1198, Dec. 1987. [6] S. M. Hanna and S. Zeroug, “Single and coupled MSW resonators for microwave channelizers,” IEEE Trans. Magn., vol. 24, no. 6, pp. 2808–2810, Nov. 1988. [7] W. S. Ishak and K. W. Chang, “Tunable microwave resonators using magnetostatic wave in YIG films,” IEEE Trans. Microw. Theory Tech., vol. 34, no. 12, pp. 1383–1393, Dec. 1986. [8] J. D. Adam and S. N. Stitzer, “MSW frequency selective limiters at UHF,” IEEE Trans. Magn., vol. 40, no. 4, pp. 2844–2846, Jul. 2004. [9] A. S. Tatarenko, V. Gheevarughese, and G. Srinivasan, “Magnetoelectric microwave bandpass filter,” Electron. Lett., vol. 42, pp. 540–541, Apr. 2006. [10] G.-M. Yang, J. Lou, J. Wu, M. Liu, G. Y. Wen, Y. Q. Jin, and X. Sun, “Dual H- and E-field tunable multiferroic bandpass filters with yttrium iron garnet film,” in Proc. Int. Microw. Symp., Baltimore, MD, 2011, pp. 1–4. [11] K.-W. Chang and W. S. Ishak, “Magnetostatic surface wave straightedge resonators,” Trans. Circuits, Syst., Signal Proc., vol. 4, no. 1–2, pp. 201–209, 1985. [12] J. H. Collins, D. M. Hastie, J. M. Owens, and C. V. Smith Jr., “Magnetostatic wave terminations,” J. Appl. Phys., vol. 49, pp. 1800–1802, 1978. [13] F. Faber, “Terminations for magnetostatic waves,” Electron. Lett., vol. 16, pp. 452–452, 1980. [14] V. L. Taylor, J. C. Sethares, and C. V. Smith Jr., “MSW terminations,” in Proc. IEEE Ultrason. Symp., 1980, pp. 562–566. [15] L. Kru and P. Edenhofer, “Broadband termination for magnetostatic surface waves,” Electron. Lett., vol. 19, pp. 971–972, 1983. [16] W. S. Ishak, “Magnetostatic surface wave devices for UHF and L band applications,” IEEE Trans. Magn., vol. MAC-19, no. 5, pp. 1880–1882, Sep. 1983. [17] T. W. O’Keeffe and R. W. Patterson, “Magnetostatic surface wave propagation in finite samples,” J. Appl. Phys., vol. 49, pp. 4886–4895, 1978. [18] V. B. Bobkov, I. V. Zavislyak, V. V. Zagorodnii, and V. F. Romanyuk, “Frequency-selective devices using surface magnetostatic waves,” Radioelectron. Commun. Systems., vol. 46, no. 5, pp. 11–17, 2003. [19] C. Kittel, Introduction to Solid State Physics. New York: Wiley, 1996.

Jing Wu (S’08) received the B.Sc. degree in electrical engineering from the University of Science and Technology of China, Hefei, China, in 2006, and the M.Sc. degree from Northeastern University, Boston, MA, in 2009, where he is currently working toward the Ph.D. degree. Since 2009, he has been a Graduate Research Assistant with the Dr. Sun’s group at Northeastern University, Boston, MA. His research interests include theory and applications of novel magnetic, ferroelectric and multiferroic materials for RFIC, monolithic microwave integrated circuits and power electronics; different RF/microwave devices, integrated tunable multiferroic electromagnetic subsystems, waves interactions in complex media, and photonic bandgap structures.

Xi Yang (S’11) received the B.Sc. degree in electrical engineering from the Shanghai Jiao Tong University, Shanghai, China, in 2008, and the M.Sc. degree from Jilin University, Changchun, China, in 2010. He is currently working toward the Ph.D. degree at Northeastern University, Boston, MA. Since 2010, he has been a Graduate Research Assistant with Dr. Sun’s group at Northeastern University, Boston, MA. His research interests include novel magnetic, ferroelectric, and multiferroic materials for microwave applications, different RF/microwave devices, and integrated tunable multiferroic electromagnetic subsystems.

Shawn Beguhn, photograph and biography not available at the time of publication.

Jing Lou received the B.S. degree in physics from Nanjing University, Nanjing, China, in 2003, and the M.S. degree in physics as and Ph.D. degree in electrical engineering from Northeastern University, Boston, MA, in 2005 and 2010 respectively. He is a Postdoctoral Research Associate with the Electrical and Computer Engineering Department, Northeastern University, Boston, MA. His main research interests include synthesis, microstructures, and properties of magnetic and magnetoelectric materials for applications in RF and microwave devices. Novel devices based on magnetoelectric concept are also his focus.

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Nian X. Sun (S’98–M’02–SM’12) received the Ph.D. degree from Stanford University, Stanford, CA, in 2002. He is currently an Associate Professor with the Electrical and Computer Engineering Department, Northeastern University, Boston, MA. Prior to joining Northeastern University, he was a Research Scientist with IBM and Hitachi Global Storage Technologies between 2001–2004. His research interests include novel magnetic, ferroelectric, and multiferroic materials, devices, and subsystems. He

has authored and coauthored over 120 publications and holds over 20 patents and patent disclosures. Dr. Sun was the recipient of the National Science Foundation CAREER Award, the Office of Naval Research Young Investigator Award, SørenBuus Outstanding Research Award, USAF Summer Faculty Fellowship, and the first prize IDEMA Fellowship. One of his papers published in 2009 was selected as the “ten most outstanding full papers in the past decade (2001–2010) in Advanced Functional Materials”. He has been an editor of the IEEE TRANSACTIONS ON MAGNETICS since 2012.

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Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity Jorge A. Ruiz-Cruz, Senior Member, IEEE, Mohamed M. Fahmi, Member, IEEE, and Raafat R. Mansour, Fellow, IEEE

Abstract—Novel combline resonators and filters with enhanced dual-band characteristics are introduced in this paper. The proposed resonator is made up of three metallic conductors: an inner post, an intermediate conductor, and an enclosure. This structure provides two asynchronous resonant modes that can be used for realizing compact microwave dual-band filters. Such dual-band filters offer the low cost, compact size, and ease of manufacturing features of traditional combline resonator filters, with additional size reduction due to the fact that a single physical cavity provides two electrical resonators. In addition, the new cavity introduces a transmission zero in the guard-bands enhancing the filter selectivity, while keeping a simple and compact inline topology. The design of filters based on this novel resonator is discussed, starting with the resonator circuit model, the coupling scheme, and the complete filter design methodology. Simulations as well as experimental results of a tenth-order dual-band filter with a measured rejection level in excess of 100 dB in the guard-band are presented to show the concept. Index Terms—Dual-resonance TEM-mode filters, multiband filters, multiconductor combline, re-entrant cross section.

I. INTRODUCTION

F

ILTERS based on combline resonators have been used in the telecommunication industry for many decades [1], [2]. In particular, they are used in wireless base-station applications because they offer low production cost with compact size and a relatively high unloaded quality factor [3], [4]. More recently, the development of multiple services and the need to use several frequency bands with more flexibility [5], [6] has triggered the demand for dual (and multiple) band filters to further improve the RF/microwave front-ends. Manuscript received July 10, 2012; revised September 19, 2012; accepted September 24, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported in part by the Spanish Government under CICYT Project TEC2010-17795, the Comunidad de Madrid Project CCG10-UAMTIC-5754, the Natural Sciences and Engineering Research Council of Canada (NSERC), COMDEV International, and the Canadian Government MITACS Accelerate Program. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17-22, 2012. J. A. Ruiz-Cruz is with the Escuela Politécnica Superior, Universidad Autónoma de Madrid, Madrid 28049, Spain (e-mail: [email protected]). R. R. Mansour is with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (e-mail: [email protected]; [email protected]). M. M. Fahmi was with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1. He is now with Nanowave Technologies. Inc., Etobicoke, ON, Canada M8W 4W3. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2223482

In conventional transceiver architectures, the use of different frequency bands leads to dedicated signal paths for each service, resulting in more volume, mass, and, eventually, higher insertion losses since more elements are involved in the RF front-end. To overcome these drawbacks, several transceiver architectures with dual (and multiple) band filters have been proposed for simplification of system architecture in different contexts [5], [6]. In base stations, dual-band filters and multiband combiners have been developed in order to achieve a more compact and effective hardware [7]. In order to address all of these applications, various dualband and multiband filters have been introduced in recent years. Dielectric resonator dual-band filters were proposed in [8] and [9], with low insertion loss due to their high unloaded . Dualband filters have been realized in other technologies, such as planar microstrip [10]–[12] and waveguide structures [13], [14], including ridge waveguide [15] or combline [16]. The dual-band filters presented in this paper are based on a novel triple-conductor combline resonator (patent pending) providing a very compact footprint while enhancing the discrimination between the two passbands by means of transmission zeros inherent in the configuration. The concept was briefly disclosed in [17]. In this paper, a detailed analysis of the novel filter configuration is presented addressing the control of the resonant modes, intra-guard-band selectivity, input/output excitation, and inter-cavity coupling. A detailed circuit modeling is also presented providing an insight on the behavior of this novel resonator structure. Simulation and measured results are given demonstrating the feasibility of realizing a compact tenth-order dual-band filter with a 100-dB rejection in the guard band. II. TRIPLE-CONDUCTOR COMBLINE RESONATOR A. Description of the Physical Configuration Fig. 1 shows the physical configuration of the introduced combline resonator. It is made up of three metallic conductors: inner post, intermediate conductor, and enclosure. The cross section shares some similarities with the re-entrant cross section in [18]. The parameters are seen in Fig. 1(d): the circular inner and length , the intermediate conmetallic post of radius , thickness and length , ductor with dimensions . In the basic resand the enclosure with dimensions onator, the intermediate conductor and the enclosure are square,

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Fig. 1. Proposed combline resonator with three metallic conductors (inner post, intermediate, and enclosure). (a) Three-dimensional view of a single metallic cavity providing two resonances and one transmission zero. (b) Half of the struccross section. (e) Example of a tenth-order ture. (c) View of the –plane. (d) filter using five of those cavities.

but they may become rectangular once the resonator becomes part of a filter to add additional variables in the filter design. The inner post and the intermediate conductors are short-circuited with the enclosure at one end, and open-ended at the other end. Their lengths , are close, but less than a quarter-wavelength at the resonant frequencies. They usually differ slightly in order to control the resonant frequency of the two resonant modes (see Fig. 2) provided by the structure for using them in dual-band filters. The proposed resonator is derived from the classical combline resonator whose electric field pattern is plotted in Fig. 2(a). The field patterns of the first two resonant modes (named from now on modes 1 and 2, respectively) in the triple-conductor resonator are shown in Fig. 2(b) and (c), respectively. Table I shows a brief comparison between both structures having the same size. It shows clearly that the spurious performance and are degraded in the triple conductor cavity in comparison with a single combline cavity with the same outer dimensions. However, the advantages offered by achieving two

Fig. 2. Electric field pattern of (a) the standard combline resonator and (b) first and (c) second resonant modes of the proposed triple-conductor combline res, , onator. Dimensions as in Fig. 1 (mm) are: , , , and .

TABLE I RESONANT FREQUENCY, UNLOADED (COMPUTED FOR ALUMINUM WITH CONDUCTIVITY 38 MS/m), RATIO OF TO VOLUME (AIR) OF THE CAVITY, AND FIRST SPURIOUS FOR THE CAVITIES IN FIG. 2. BOTH CAVITIES HAVE THE SAME INNER POST AND OUTER DIMENSIONS; THE TRIPLE-CONDUCTOR COMBLINE HAS AN INTERMEDIATE CONDUCTOR BETWEEN THEM

resonant modes per single cavity offer a good tradeoff. In the case of filters based on this novel resonator, specifically the implementation of dual-band filters, the use of these resonators eliminates the need for additional input/output combining networks that are necessary if single combline cavities were to be used. In addition, the enhanced guard-band selectivity provided by the transmission zeros inherent to the resonator is another clear advantage that will be shown later. As for the reduction of the spurious-free window of the resonator, improvement in

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B. Circuit Model for the Triple-Conductor Resonator

Fig. 3. Equivalent circuit model of the triple-conductor resonator. (a) Two-port problem associated with the resonator. (b) Equivalent circuit model. (c) Unfolded circuit showing the input reflection coefficient for computing the resonant frequencies and showing the total voltages and currents in the transmission lines.

the spurious performance could be achieved by using stepped impedance resonator methodologies [19]. The field configuration in Fig. 2(a) can be explained in terms of the TEM mode supported by the two-conductor transmission line (post and enclosure). The TEM is short-circuited at one end, while at the other end finds a discontinuity (the open), exciting higher order modes with electric field z-component in the vicinity of the open region. The equivalent circuit model of the standard combline resonator is thus a transmission line loaded with a capacitor responsible for the energy stored in these evanescent modes of the problem. The loading provides a resonant frequency lower than that corresponding to the quarter wavelength of the post length. At a transversal plane [as in Fig. 1(c)] sufficiently far from the open (and thus where the field z-components are negligible), the field pattern of the resonant mode is basically that of the TEM mode in the transmission line [left side of Fig. 2(a)]. The field configurations for the triple-conductor combine resonator in Fig. 2(b) and (c) share many of these features but they have some particularities that will be explained with the equivalent circuit model in Fig. 3.

The resonator in Fig. 3(a) can be described as the cascading of several sections of homogenous waveguides along . The cross section of the first section is shown on the right-hand side of Fig. 3(a). There are three conductors, and thus it is well known that, in such a case, the structure supports two TEM modes, whose characterization will be described now. Two completely isolated 2-D domains can be identified in the cross section in the right-hand side of Fig. 3(a): internal region I and external region E. For the equivalent circuit, region I is the cross section of an ideal transmission line with characteristic impedance corresponding to the fundamental TEM mode, named , which exists between the inner cylindrical conductor named c and the intermediate conductor named b. Similarly, region E is the cross section of another ideal transmission line with characteristic impedance corresponding to the mode , which exists between the intermediate conductor named b and the outer conductor named a. These two ideal transmission lines encounter a waveguide discontinuity at a reference plane located at , where higher order modes will be excited. The combined effects of the higher order modes interaction with the two ideal transmission lines representing and can be modeled using a pi-network composed of three capacitances shown in Fig. 3(b). The equivalent circuit of the entire resonator is also shown in Fig. 3(b). It is worth noting that and in Fig. 3 are artificial ports created to be used with the circuit model. The domain of definition for port is region E (I) at . These ports will be short-circuited to find the resonant modes of the problem, as indicated in Fig. 3(b) and (c). Moreover, depending on the relative length between the inner and intermediate conductor, there are two possible cases for shown at the bottom of Fig. 3(a), yielding . In order to calculate the parameters of the proposed equivalent circuit model, the two-port ( and ) simulation of the structure in Fig. 3(a) is performed using Ansoft High-Frequency Structure Simulator (HFSS). The process involves a simple process in two steps. First, the two-port -parameters at the center frequency of the design band are de-embedded to , and transformed to ABCD parameters. Second, the capacitors of the pi-network are extracted at the center frequency by the usual relations from the ABCD matrix of the circuit network as (1) Fig. 4(a) shows the full-wave analysis for a typical resonator and the response using the extracted circuit following the process aforementioned. The circuit in Fig. 3 provides very good matching with the full-wave response in the whole frequency band. The different parameters of the circuit model are shown in Fig. 4(b) for several physical dimensions of the resonator. The characteristic impedances of the two transmission lines , are also plotted in the same figure. The values correspond to a triple-conductor resonator having always the same enclosure, but changing the size of the intermediate conductor.

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Fig. 4. (a) Comparison between the full-wave simulation (solid line; reference plane for the phase in , ) and the response of the extracted circuit (with . (b) Extracted circuit parameters for markers) for a typical case with different dimensions of , and . Other data are as in Fig. 2.

Fig. 5. Field configuration of the first (mode 1) and second (mode 2) resonant . modes of the triple-conductor combline resonator for Other data are as in Fig. 2.

C. Resonant Modes and Field Pattern Configuration By characterizing the elements of the ideal circuit, resonant frequencies of the structure as well as voltage and current distributions along the resonator can be easily calculated. The basic circuit to solve is shown in Fig. 3(c), where all parameters can be obtained following the previous Section II-B. The reflection coefficient at the input port when port is short-circuited can be easily solved at any frequency. Then, the resonant frequencies are obtained when the phase of the reflection coefficient is an odd multiple of 180 as follows: (2) The characteristic function is plotted in the top of Figs. 5 and and , re6 for two different configurations ( spectively). It can be seen that the behavior of the phase is very similar in both cases, with two close resonant frequencies. Additional values are presented in Table II, where the results obtained by solving (2) and by the eigenmode solver of the HFSS show very good agreement. Once the resonant frequencies have been found by solving (2), the voltage and current distribution of each corresponding resonant mode can be easily solved at any point of the circuit. This is shown in Figs. 5 and 6 for both resonant mode 1 (the one with lower frequency) and resonant mode 2 (higher frequency). In Fig. 5, it can be easily seen that mode 1 is mostly confined in the external region E, with stray fields in region I. This resonant

Fig. 6. Field configuration of the first and second resonant modes for . Other data are as in Fig. 2.

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TABLE II RESONANT FREQUENCIES OF RESONANT MODES 1 AND 2 FOR DIFFERENT VALUES OF THE CONDUCTOR LENGTHS (OTHER DATA AS IN FIG. 2), COMPUTED BY THE FULL-WAVE EIGENMODE SOLVER (HFSS) AND USING THE EQUIVALENT CIRCUIT MODEL SOLVING (2)

mode is a combination of for region E (more intense) and for region I. On the other hand, mode 2 is mostly confined in the internal region, as it is also a combination of and , the contribution of which now is more dominant. A very similar pattern was obtained in Fig. 2 for . Moreover, the electric field points in the same direction in both regions E and I for mode 1 and in opposite directions for mode 2. This pattern also holds for Fig. 6 and for all of the analyzed configurations. One important observation is the dependence of the relative field intensities in different regions on the relative length of the inner post and the intermediate conductor. When the inner post is longer than the intermediate conductor (Fig. 6), the field in the region E for mode 2 becomes more significant. Fig. 6 can be compared with the very weak outer field in Figs. 2 or 5 for mode 2, where the intermediate conductor was equal or longer than the post, respectively. Thus, the relative length of the conductors (and also the separation between them) provides a mechanism of controlling the distribution of the field in the outer and internal regions. This is crucial for using the resonator in filter designs, since this provides the means to couple resonant modes from separate cavities, otherwise almost fully isolated, through the presence of stray fields. The circuit model provides physical insight to the resonator and justifies the resonant frequencies (see Table II) and field distribution that can be also obtained by full-wave eigenmode analysis using HFSS. Moreover, it also shows that the characteristic function, for the usual values in design, always follows the same pattern and has anti-resonance between the two modes. This will lead to the presence of a transmission zeros in the filter design. The variation of anti-resonant frequency for several physical dimensions is plotted in Fig, 7, along with other parameters that summarize the performance of the resonator. When the intermediate conductor becomes very close to the enclosure, the first higher order mode for the filter (mode 3 in our case) becomes closer to mode 2. A challenging issue revealed by these parametric sweeps is the fact that the length of both conductors significantly affects both resonant frequencies at the same time (they are not controlled independently by the different lengths , ).

Fig. 7. Main parameters of the triple-conductor resonator when the size and length of the intermediate conductor (keeping same enclosure) are changed. Data are as in Fig. 2.

It is observed in Fig. 7 and in Table I that the quality factor of the two modes are different and lower than that of a standard combline resonator with the same enclosure size. The anti-resonance takes place at a frequency between the two resonant frequencies, which makes the two modes suitable for use in filters with two separate passbands. For achieving approximately the same of the standard resonator in Table I for the two modes, the enclosure and spacing between conductors have to be increased. This also separates the resonant frequencies and (see Fig. 7). A new configuration, which provides and , is obtained with , , , , and (dimensions in millimeters). In this case, the new resonant frequencies of the two modes in the triple-conductor combline are 1.78 and 2.75 GHz. Their is 0.067/mm and 0.075/mm , respectively. An alternative comparison keeping the same enclosure and similar resonant frequencies for the two modes with respect to the standard combline was presented in Table I. III. RESONATOR COUPLING The excitation of a standard combline resonator can be done by several ways. One common option is to use a coaxial cable whose inner conductor is tapped in to the inner metallic post by a probe, while the coaxial outer conductor is connected to the enclosure. A similar scheme could be used for the triple-conductor combline, tapping in a probe from the external coaxial to the inner post and the intermediate conductor. However, the mechanical arrangement for the connection to the inner post is more complicated, and the simplest scheme was explored

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Fig. 8. Input coupling to mode 1 and 2 by a tapped-in coaxial to the intermediate conductor. Structure (a), model (b) and coupling parameter and loaded resonant frequency (c). Data as in Fig. 2.

in Fig. 8, with a direct connection only to the intermediate conductor. The circuit model in Fig. 8(b) has a source node coupled to resonant modes 1 and 2. In order to extract the input coupling to both resonant modes, the group delay of the input reflection coefficient obtained from the full-wave simulation of Fig. 8(a) is matched with the circuit response from the circuit model in Fig. 8(b). The good matching between both responses for a typical case is shown in Fig. 8(b). In Fig. 8(c), it is seen that this simple configuration (as simple as for a standard combline) provides sufficient variation of the input coupling to both resonant modes. The design variables are the length of the probe and the tap-in height. Nevertheless, it is also seen in the same figure that these two variables affect significantly both couplings at the same time; there is not a single correspondence between a

Fig. 9. Coupling between the modes of two cavities by a window of 15-mm height opened at the intermediate conductor. (a) Structure. (b) Loose input coupling for getting the inter-cavity couplings. (c) Coupling and loaded resonant , , and frequency. Main dimensions (mm) are: (other data are as in Fig. 2).

variable and a filter parameter, and additional dimensional variables will be used for design. Fig. 9 shows the setup used to characterize the coupling between two different cavities. For this initial coupling computation, it is assumed that resonant mode 1 (2) of the first cavity only interacts with resonant mode 1 (2) of the second cavity. In this case, using a very loose input/output coupling, the full-wave response of the structure has four clear peaks shown in Fig. 9(b). Using these peaks, the coupling coefficients are computed by the relations

(3)

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Fig. 10. Coupling by an electric probe: half of a four-pole filter showing the probe, the wall to isolate the cavities, and the full-wave response by HFSS.

The simplest way to couple two standard combline resonators is by controlling the space between them. The same can be done for the triple-conductor combline, although the coupling for mode 2, which is usually more concentrated in the internal region I, will drop when the cavities are far apart. In the limiting case when mode 2 is essentially confined between the intermediate and inner conductor, a more suitable coupling topology would be to consider that one cavity is only coupled to the adjacent cavity by mode 1 and that mode 2 is only coupled to mode 1 in each cavity, as the topology shown in [16, Fig. 10]. Nevertheless, mode 2 can be more exposed to adjacent cavities by opening a window in the intermediate conductor in Fig. 9(a), which provides the adjacent couplings for both modes in Fig. 9(c). The window, along with an inner post longer than the intermediate conductor, allows increasing the coupling for mode 2. In Fig. 9(b), two transmission zeros between the passbands are observed. This can be explained using the circuit model: each cavity is introducing a transmission zero. In addition to the coupling schemes discussed in this section, other types used in standard combline structures could also be used here. For instance, Fig. 10 shows a fourth-order filter with an electric probe between the cavities, using a metallic wall opened at the top to control the amount of magnetic field interacting between the two cavities. The structure shows two transmission zeros in the guard band. This simple four-pole design will be complemented in Section IV with the methodology for addressing higher order dual-band filters.

IV. DESIGN AND EXPERIMENTAL RESULTS A considerable amount of research dealing with all aspects of the synthesis problem for dual-band filters has been recently published. Analytical methods and optimization techniques have been presented to reach a coupling matrix fulfilling a desired set of specifications. One common approach is to synthesize two bands in a wideband large-order filter (see, for instance, [10], [14], and [20]), using cross couplings to create the guard-band in-between. Although this technique allows the use of any type of resonator, such a concept provides a minor size reduction with little cost savings, since it is equivalent to having two filters combined together to construct a dual-band filter. For example, if a three-pole filter is needed for each band, six resonators are used to realize a wideband filter with trans-

Fig. 11. Extracted response [coupling matrix in (4)] for the dual-band sixthfilter, compared with the full-wave response and the measured order response.

mission zeros creating a guard-band in-between to effectively realize a dual-band filter. A clear advantage of the developed triple-conductor combline resonator is its compactness, at the expense of and spurious performance. In the provided degradation in designs, the number of the cavities is reduced to half of the total order of the filter in comparison with designs that use dedicated resonators [14], [15]. In addition, the guard-band selectivity is enhanced by means of the transmission zeros inherent to each cavity. No combination networks are used at the input/output of the filter, with coaxial excitation tapped in to the external conductor of the input/output triple-conductor cavity. Two - and tenth -order filters, design examples, sixth will be shown where we effectively use the triple-conductor combline resonator as the basic building block, exploiting its resonant modes 1 and 2 for each passband. A. Sixth-Order

Dual-Band Filter

The triple-conductor combline resonator has field configurations that are suitable for realization of filters with the lower frequency band having larger fractional bandwidths than the higher frequency band. Nevertheless, a sixth-order filter was presented in [17], where the bands were of the same order. The filter had three poles per passband, centered at 1.85 and 2.15 GHz, with 20-dB return loss and 70- and 50-MHz bandwidths. The results of that filter have been further analyzed in order to extract the actual coupling scheme that exists in the structure due to the proximity of the resonators. The measured response in Fig. 11, showing excellent agreement with the full-wave response, has been used to extract the coupling matrix that captures the desired and parasitic couplings of the filter [21], [22].

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The coupling matrix representing the structure is given in (4), shown at the bottom of the page. The ideal circuit response based on (4) is also shown in Fig. 11 and shows good agreement with both simulated and measured results. It can be observed that the topology has two main signal paths for each passband, identified by the couplings with the largest values and represented in Fig. 11(b), and stray couplings. Dual-Band Filter

B. Tenth-Order

Ideal circuit synthesis techniques [22]–[24] were used to obtain a tenth-order filter that has two passbands: the first one with 75-MHz bandwidth centered at 1.88 GHz and the second one with 60-MHz bandwidth centered at 2.185 GHz. Both bands have a return loss of better than 20 dB. A guard band is sought with better than 60 dB of rejection in the band from 1.975 to 2.075 GHz. A coupling matrix was obtained, conforming to the topology shown in Fig. 12(b) and assuming only longitudinal couplings between similar modes. The coupling matrix is given by (5), shown at the bottom of the page, and its response is shown in Fig. 12(a). The initial couplings for the filter were obtained from the structures used in Section III. A full-wave optimization was used to obtain the final filter response, using such optimization for each resvariables as the lengths of the conductors , onator, the size of the intermediate conductors , , and their

Fig. 12. Synthesized response (a) for the tenth-order coupling scheme. (b) Coupling matrix in (5).

filter with the

associated windows, the height and length of the input/output probe, and the separation between cavities.

GHz MHz

(4)

GHz MHz

(5)

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Fig. 13. (a) Layout of the tenth order filter (b) Manufacturing by three parts (c) Photograph of the 10th order filter.

The final configuration of the filter is shown in Fig. 13, and its full-wave response is found in Fig. 14, along with the measurements. The two-dimensional (2-D) layout of the designed filter is shown in Fig. 13(a). The filter was manufactured by regular milling of three separate parts shown in Fig. 13(b). The filter was made out of Aluminum. In this prototype, no tuning was used (flat cover), since the tolerances were sufficient for this frequency band and the rounded corners in the intermediate conductor and the enclosure did not affect the response much. The most sensitive dimensions are the conductor lengths controlling the resonant frequencies. In other frequency bands where fabrication tolerances can be more important, tuning elements can be used as in other combline filters. The measured results are shown in Fig. 14. The rejection behavior below and above the two passbands follows the skewed dispersion effects observed in standard combline filters. Very good rejection was achieved at the guard band, reaching 100 dB, due to the transmission zeros inherent in the structure. This high selectivity is also reflected in the peak of the group delay (see Fig. 14(d) at the upper end of the first passband). Excellent agreement between the theoretical response and the measurement is observed. The broadband response in Fig. 14(b) shows the first spurious at 4.2 GHz, in agreement with the first higher order mode computed in Fig. 7. The in-band insertion loss is approximately 0.5 dB for the lower band and 0.6 dB for the upper band, which agrees with the theoretical simulation taking into account the finite conductivity of the Aluminum [see Fig. 14(c)]. This level of the insertion loss indicates an unloaded approximately of 1700 for the resonant modes in the triple-conductor combline structure.

Fig. 14. Experimental results of the dual-band dual-resonance combline tenthfilter, compared with the theoretical response (dashed lines). (a) order In-band response. (b) Broadband response. (c) Details of the insertion loss (sim38 MS/m). (d) Group delay. ulations with

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V. CONCLUSION This paper has presented a novel combline structure having three conductors and providing two resonant modes with different field patterns and well-characterized resonant frequencies. In comparison with standard combline resonators, having an additional conductor is shown to be suitable for designing dual-band filters with enhanced selectivity in the guard band. The concept has been demonstrated with the full design of sixth- and tenth-order dual-band filters. These filters harness the advantages of the compact low-cost combline filter technology, with further reduction in size. It promises to be useful in emerging dual-band wireless base-station filter applications. ACKNOWLEDGMENT The authors want to acknowledge the reviewers, especially the third one, for his helpful suggestions and comments on the coupling topology. REFERENCES [1] G. L. Matthaei, “Comb-line band-pass filters of narrow or moderate bandwidth,” Microw. J., vol. 6, pp. 82–91, Aug. 1963. [2] R. J. Wenzel, “Synthesis of combline and capacitively loaded interdigital bandpass filters of arbitrary bandwidth,” IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 8, pp. 678–686, Aug. 1971. [3] R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems Fundamentals, Design, and Applications. New York: Wiley-Interscience, 2007. [4] R. R. Mansour, “Filter technologies for wireless base stations,” IEEE Microw. Mag., vol. 5, pp. 68–74, Mar. 2004. [5] S. Holme, “Multiple passband filters for satellite applications,” in Proc. 20th ALAA Int. Commun. Satellite Syst. Conf Exhibit, 2002, paper AIAA-2002-1993. [6] H. Hashemi and A. Hajimiri, “Concurrent multiband low-noise amplifiers-theory, design, and applications,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 1, pp. 288–301, Jan. 2002. [7] G. Macchiarella and S. Tamiazzo, “Dual-band filters for base station multi-band combiners,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007, pp. 1289–1292. [8] R. Zhang and R. R. Mansour, “Dual-band dielectric-resonator filters,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 7, pp. 1760–1766, Jul. 2009. [9] M. Memarian and R. R. Mansour, “Dual-band half-cut dielectric resonator filters,” in Proc. 39th Eur. Microw. Conf., Sep. 2009, pp. 555–558. [10] M. Mokhtaari, J. Bornemann, K. Rambabu, and S. Amari, “Coupling matrix design of dual and triple passband filters,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 11, pp. 3940–3946, Nov. 2006. [11] B. Chen, T. Shen, and R. Wu, “Design of tri-band filters with improved band allocation,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 7, pp. 1790–1797, Jul. 2009. [12] A. Garcia-Lamperez and M. Salazar-Palma, “Single-band to multiband frequency transformation for multiband filters,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 12, pp. 3048–3058, Dec. 2011. [13] S. Amari and M. Bekheit, “A new class of dual-mode dual-band waveguide filters,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 8, pp. 1938–1944, Aug. 2008. [14] Y. Zhang, K. A. Zaki, J. A. Ruiz-Cruz, and A. E. Atia, “Analytical synthesis of generalized multi-band microwave filters,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007, pp. 1273–1276. [15] M. M. Fahmi, J. A. Ruiz-Cruz, R. R. Mansour, and K. A. Zaki, “Compact wide-band ridge waveguide dual-band filters,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2010, pp. 888–891.

[16] G. Macchiarella and S. Tamiazzo, “Design techniques for dual passband filters,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 11, pp. 3265–3271, Nov. 2005. [17] J. A. Ruiz-Cruz, M. M. Fahmi, and R. R. Mansour, “Dual-resonance combline resonator for dual-band filters,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [18] S. B. Cohn, “The re-entrant cross section and wide-band 3-dB hybrid couplers,” IEEE Trans. Microw. Theory Tech., vol. MTT-11, no. 4, pp. 254–258, Jul. 1963. [19] H.-W. Yao, K. A. Zaki, A. E. Atia, and T. Dolan, “Improvement of spurious performance of combline filters,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 1997, pp. 1099–1102. [20] S. Bila, R. J. Cameron, P. Lenoir, V. Lunot, and D. Seyfert, “Chebyshev synthesis for multi-band microwave filters,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 1221–1224. [21] M. Meng and K.-L. Wu, “An analytical approach to computer-aided diagnosis and tuning of lossy microwave coupled resonator filters,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 12, pp. 3188–3195, Dec. 2009. [22] S. Amari, U. Rosenberg, and J. Bornemann, “Adaptive synthesis and design of resonator filters with source/load-multiresonator coupling,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 8, pp. 1969–1978, Aug. 2002. [23] S. Amari, “Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 9, pp. 1559–1564, Sep. 2000. [24] M. Mokhtaari, J. Bornemann, K. Rambabu, and S. Amari, “Couplingmatrix design of dual and triple passband filters,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 11, pp. 3940–3946, Nov. 2006.

Jorge A. Ruiz-Cruz (SM’11) received the Ingeniero de Telecomunicación and Ph.D. degrees from the Universidad Politécnica de Madrid, Madrid, Spain, in 1999 and 2005, respectively. Since 2006, he has been with the Universidad Autónoma de Madrid, Madrid, Spain, where in 2009 he became an Associate Professor. His current research interests are the computer-aided design of microwave passive devices and circuits (e.g., filters, multiplexers, and ortho-modes).

Mohamed M. Fahmi (S’05–M’09) received the B.Sc. degree (with Honors) in electronics engineering from Mansoura University, Mansoura, Egypt, in 1999, the M.Sc. degree from Howard University, Washington, DC, in 2003, and the Ph.D. degree from the University of Maryland, College Park, in 2007. From 1999 to 2000, he was a Teaching/Research Assistant with the Department of Electronics Engineering, Mansoura University, Mansoura, Egypt. From 2001 to 2003, he was a Research Assistant with the Department of Electrical and Computer Engineering, Howard University , Washington, DC. From 2003 to 2007, he was a Teaching/Research Assistant with the Department of Electrical and Computer Engineering, University of Maryland, College Park, where he was a Postdoctoral Researcher from January to July 2008. From September 2008 to January 2012, he was with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada, as a Post-Doctoral Fellow. In February 2012, he joined Nanowave Technologies Inc., Etobicoke, ON, Canada, as a Microwave Engineer. His current research interests include computer-aided design of microwave devices.

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Raafat R. Mansour (S’84–M’86–SM’90–F’01) was born in Cairo, Egypt, on March 31, 1955. He received the B.Sc. (with honors) and M.Sc. degrees from Ain Shams University, Cairo, Egypt, in 1977 and 1981, respectively, and the Ph.D. degree from the University of Waterloo, Waterloo, ON, Canada, in 1986, all in electrical engineering. In 1981, he was a Research Fellow with the Laboratoire d’Electromagnetisme, Institut National Polytechnique, Grenoble, France. From 1983 to 1986, he was a Research and Teaching Assistant with the Department of Electrical Engineering, University of Waterloo, Waterloo, ON, Canada. In 1986, he joined COM DEV Ltd., Cambridge, ON, Canada, where he held several technical and management positions with the Corporate

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Research and Development Department. In 1998, he received the title of a Scientist. In January 2000, he joined the University of Waterloo as a Professor with the Electrical and Computer Engineering Department. He holds a Natural Sciences and Engineering Research Council of Canada (NSERC) Industrial Research Chair in RF engineering with the University of Waterloo. He is the Founding Director of the Center for Integrated RF Engineering (CIRFE), University of Waterloo. He has authored or coauthored numerous publications in the areas of filters and multiplexers, high-temperature superconductivity, and microelectromechanical systems (MEMS). He is a coauthor of a book, Microwave Filters for Communication Systems (Wiley, 2007). He holds several patents related to areas of dielectric resonator filters, superconductivity, and MEMS devices. His current research interests include MEMS technology and miniature tunable RF filters for wireless and satellite applications. Dr. Mansour is a Fellow of the Engineering Institute of Canada (EIC).

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Narrowband Microwave Filters With Mixed Topology Giuseppe Macchiarella, Senior Member, IEEE, Matteo Oldoni, and Stefano Tamiazzo

Abstract—Narrowband microwave filters exhibiting transmission zeros in the response (either imaginary and/or complex) can be typically designed with cross-coupled or extracted pole topologies. These configurations have advantages and disadvantages that must be carefully considered during the choice of a specific topology. In some cases, however, it may be convenient to choose a mixed topology, i.e., part of the structure with an extracted-pole and part with a cross-coupled configuration. Unfortunately, even if several well-established techniques are available in the literature for the cross-coupled or extracted-pole synthesis taken separately, nothing can be found for the design of mixed topology filters (apart direct optimization). In this study, two solutions for the synthesis of a low-pass prototype with a mixed topology are presented, which noticeably increases the design flexibility of narrowband microwave filters. Several examples are presented for illustrating the proposed techniques for the synthesis of mixed-topology prototype filters. A test filter, synthesized with the second method introduced and fabricated in coaxial technology, has given an experimental validation of the proposed technique. Index Terms—Cross-coupled filters, extracted pole filters, filters synthesis.

T

I. INTRODUCTION

HE DESIGN of narrowband microwave filters with arbitrary transmission zeros is generally considered a mature subject, with well-assessed solutions available in the literature [1]–[11]. In fact, the most popular topological configurations, generally referred to as cross-coupled [1]–[6] and extractedpole [7]–[10], can be easily designed starting from the synthesis of a low-pass prototype and deriving suitable de-normalized parameters (coupling coefficients) that allow a first-order dimensioning of the physical structure implementing the filter [11], [12]. It is worth observing that, even if the extracted-pole filters contain NRNs [9], it is, however, possible to characterize this topological configuration by means of universal parameters (generalized coupling coefficients) that are independent of the absolute values of the circuit components [13] and uniquely represent the filter (as in the case of classical coupled-resonators filters). The same formal characterization is then possible for both basic topologic configurations of microwave filters mentioned above. Manuscript received June 15, 2012; revised August 29, 2012; accepted September 04, 2012. Date of publication October 10, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. G. Macchiarella and M. Oldoni are with the Politecnico di Milano, Dipartimento di Elettronica e Informazione, 20133 Milan, Italy (e-mail: [email protected]). S. Tamiazzo is with Commscope, Agrate Brianza, Province of Monza and Brianza 60541, Italy (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2218121

The choice of one of these configurations must be carefully evaluated because it has a strong impact on the achievable electrical characteristic and on the possible issues related to the filter implementation. For instance, the extracted-pole topology does not allow the inclusion of complex transmission zeros in the filter response (useful for phase equalization purposes). Moreover, the practical implementation of NRNs required by this topology may be problematic for some fabrication technology. On the other hand, a good feature of the extracted-pole configuration is the easy tunability of the filters (the resonant frequency of the extracted resonators coincides with the imposed transmission zeros). It is then understandable that, in several situations, a mix of the two basic topologic configurations could be a great advantage for the designer, i.e., to realize part of the filter with the extracted-pole topology and part with the cross-coupled configuration. However, until recently [14], there are no references to mixed synthesis in the literature (apart from a brief comment on a possible approach in [11, p. 354]). The aim of this study is to extend what is presented in [14] by illustrating in details two approaches to the synthesis of a low-pass prototype with a mixed topology. In the next sections, after a brief recall on the general characterization of a low-pass prototype, including both types of configurations (cross-coupled and extracted-pole), the proposed techniques are described with examples illustrating their potentiality. Finally, an experimental test filter has been used for validating the second presented approach. II. GENERALIZED COUPLING MATRIX FOR LOW-PASS PROTOTYPES WITH MIXED TOPOLOGY The normalized low-pass prototype of a generic cross-coupled filter of order is typically described by the normalized coupling matrix of order [6]. This matrix contains the frequency-invariant part of the -port admittance matrix of the filter (defined at the resonators ports). It is assumed that the frequency-dependent part is constituted by a vector containing unit capacitances (plus 0 in the first and last positions). A typical configuration of the low-pass prototype of an extracted pole filter is depicted in Fig. 1 in the case of a number of transmission zeros equal to the number of resonators (a conventional schematization is adpoted [10]). As can be observed, it includes nonresonating nodes (NRNs) constituted by frequencyinvariant susceptances, which are coupled, through admittance inverters, either to resonant nodes (unit capacitance) or to other NRNs (other than to load and source). This network can also be represented by means of a normalized coupling matrix of order , where is the overall number of nodes (resonating, nonresonating, source, and load). The overall matrix can be defined as in the previous case, i.e.,

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(1)

MACCHIARELLA et al.: NARROWBAND MICROWAVE FILTERS WITH MIXED TOPOLOGY

Fig. 1. Typical topology of an extracted-pole low-pass prototype. Black node represents unit capacitance in parallel with frequency invariant susceptance. Dashed nodes are frequency-invariant susceptances. Black lines are admittance inverters.

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Fig. 3. Initially synthesized prototype (numbers represent the element of the normalized coupling matrix ).

Fig. 2. Transformation of a triplet into an extracted-pole block. Note that the two blocks are, in general, part of an arbitrary cross-coupled network (represented by the dots in the figure).

where is the normalized frequency and is a vector of length , containing 1’s and 0’s according to the type of node at each position. The low-pass network obtained by means of the usual synthesis techniques [10], [11] must, in general, be scaled in order to satisfy the convention assumed in the definition of . Using the above general convention, a low-pass prototype with a mixed topology can represented by the matrix defined as above (together with the vector , which specifies the node type). Even if such a matrix is not unique, the generalized coupling parameters derivable from [13] uniquely define the mixed-topology configuration. III. MIXED TOPOLOGY BY MEANS NETWORK TRANSFORMATIONS

Fig. 4. Final transformed prototype with mixed topology (underlined numbers modified respect to ). represent the element of

Note that the unit capacitances of the resonant nodes are not affected by the transformation. The above transformation can also be applied when node 1 represents the source (or node 3, the load); in these cases, however, a susceptance (NRN) will appear in parallel to the source (or load). These susceptances can be removed by modifying the element and the coupling (or ) as follows:

OF

A simple (but limited) method to realize a mixed topology consists of the transformation of parts of a low-pass prototype synthesized with the cross-coupled topology. For instance, in [15], it is shown how to transform a cascaded singlet (NRN coupled to a resonant node) into a triplet block. In a similar way, it is possible to derive analytically the relationships between the elements of a triplet block and those of an extracted-pole block (Fig. 2). This derivation is based on the well-known -totransformation [17]. Assume that the initially synthesized network contains a triplet characterized by the coupling matrix . The elements of the coupling matrix referring to the extracted-pole block (Fig. 2) can then be computed with the following equations:

(2)

(3)

As an example, let consider a prototype of order 6 with four transmission zeros (two imaginary and two real): Return Loss: 26 dB . The low-pass prototype with the generalized Chebyshev response is initially synthesized from the characteristic polynomials with the cascaded-block topology shown in Fig. 3 [16]. Note that a similar filter cannot be realized with the extracted pole topology due to the presence of the real zeros. A mixed topology is instead allowed by assigning the complex zeros to the inner quadruplet and substituting the two outer triplets with extracted blocks. Applying the transformation depicted in Fig. 2 [with (3)], the new prototype shown in Fig. 4 is obtained. Fig. 5 shows the computed response, which obviously is the same for both networks (Figs. 3 and 4).

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Fig. 6. Block division of the prototype to be synthesized.

Fig. 5. Computed response of synthesized prototypes (Figs. 3 and 4).

The previous transformation can also be applied to the de-normalized prototype in the bandpass frequency domain; it is then possible to obtain equations similar to (2) and (3), expressing the de-normalized parameters of the transformed topology (these equations are reported in the Appendix). It must be observed that the method just outlined has some limitations. First of all, only topologies realizable with a cascaded block structure can be considered (then fully canonical filters are excluded). Moreover, it is not possible to obtain two extracted-pole blocks directly cascaded in the transformed topology (at least one resonating node must be present in between the two blocks). To overcome these limitations, a more general solution is presented in Section IV. Note that the developed procedure is completely analytical (i.e., does not resort to any kind of numerical optimization). IV. DIRECT SYNTHESIS OF MIXED PROTOTYPES It is assumed that the prototype to be synthesized is represented by the cascade of three two-port subnetworks called (Fig. 6). Networks and are assumed to belong to the extracted-pole category, while network has a cross-coupled configuration. The first step of the procedure consists in the evaluation of the characteristic polynomials of the filter, associated to the electrical requirements (return loss (RL), overall degree , assigned transmission zeros ). The order (number of poles) and the zeros to be extracted are then specified for each block as follows: Block

number of poles imaginary zeros

Block

number of poles complex zeros

Block

number of poles imaginary zeros

with the obvious conditions and . Note that the zeros to be extracted by and must be pure imaginary.

Fig. 7. Topology of the extracted blocks

.

The following step of the procedure consists of the extracted-pole synthesis of network , starting from the characteristic polynomials of the filter , the transmission zeros , and the number of poles assigned to ; note that the sequence of zeros extraction must be specified (it defines the block topology). The extracted-pole synthesis is carried out by means of the polynomial matrix [computed from the characteristic polynomials ] using techniques well outlined in the literature [10], [11]. At the end of the extraction process, other than the elements of the network , the polynomial matrix defining the block in Fig. 6 [characterized by polynomials ] is also available. Note that the roots of represent the transmission zeros to be extracted by the blocks and . The synthesis process is then repeated for extracting the network ; the extracted-pole synthesis starts in this case from the output port of yielding, once completed, the synthesized parameters of the networks and the polynomials referring to the network . Finally, the characteristic polynomials and associated to the network are obtained using the following expressions:

(4) can be now synthesized with a cross-coupled The network topology (from the polynomials ), using one of several methods available in the literature [16]. A. Generation of the Coupling Matrix From Blocks An example of typical topology for the blocks and is schematized in Fig. 7. It is assumed that the last element must extract a zero (further cascaded resonating nodes are assigned, as poles, to block ). The synthesized elements are constituted by capacitances in parallel to frequency invariant susceptances (black nodes in Fig. 7), nonresonating susceptances (dashed nodes), and admittance inverters (solid lines). From these elements,

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Fig. 9. Synthesized blocks

Fig. 8. (a) Topology of the inner block in case of fully canonical. (b) Equivalent circuit for the phase shifter (frequency invariant).

.

Finally, it must be remarked that with order of matrix increases to

fully canonical, the .

V. EXAMPLES As a first example, consider the following assignments:

with suitable scaling, the normalized coupling matrix can be derived following the guidelines given in Section II. Note that the order of is and the order of is ( includes the source and the load). The synthesis of the cross-coupled network produces the coupling matrix of order ; in fact, the last node of and the first node of represent the source and load for this matrix. The overall matrix of the mixed-topology prototype has order and is generated by suitably combining ; note that the null elements and are replaced into by and . It can be observed that the procedure can also be easily applied with block (or ) removed; in this case, the output (input) of the mixed network coincides with the output (input) of block . B. Special Case: Block

Fully Canonical

and As previously observed, the connection of blocks to block is accomplished by assuming that the source and load of coincide, respectively, with the last node of and the first node of . However, when is a fully canonical block (i.e., the number of poles is equal to the number of zeros ), an additional phase rotation (frequency invariant) is required at input and output of . This can be obtained with two phase shifters, implemented through the network shown in Fig. 8. The requested rotation angles and of the two phase shifters are obtained from the highest degree coefficient of polynomials and (the latter is obtained from the roots of with the real parts of opposite sign [11])

Note that and are always real numbers when is not fully canonical (thus, ). After evaluating the elements and from equations in Fig. 8, two additional inverters ( and ) are introduced between the last node of and the first node of ; moreover, and are added to the susceptances associated to these nodes (nonresonating).

Order Return loss

dB

Transmission zeros This is a fully canonical filter with four imaginary and two real zeros, which we want to implement with the topology in Fig. 6 and the following parameters: Network Network Network

quadruplet

Note that the solution of Section III cannot be used because networks and are realized by two directly connected nodes, each of which extracts one transmission zero. The synthesis procedure starts with the evaluation of the characteristic polynomials of the whole filter and yields

It can be observed that polynomial is not monic (due to the fully canonical condition). As a consequence, two phase shifters will be needed between blocks – and – . After computing the polynomial chain matrix from , the synthesis of the networks and is performed, yielding the result shown in Fig. 9 (the numbers represent the elements of the normalized coupling matrix). From the residual chain matrix, the characteristic polynomials of block are then computed as follows:

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Fig. 10. Synthesized block

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

. Fig. 13. Prototype synthesized for the second example. Block and implements two real transmission zeros.

is of order 4

Fig. 11. Final prototype with mixed topology.

Fig. 14. Prototype of the second example with of sixth degree.

Fig. 12. Computed response of the synthesized prototype with mixed topology.

The network , synthesized with a quadruplet block, is shown in Fig. 10. It can be observed that two nodes of the quadruplet represent, in this case, the source and load of the block (zero shunt susceptances); moreover, since the block is fully canonical, two phase shifters with rotation angles reported in Fig. 10 must be included. These are then implemented with the equivalent circuit of Fig. 8, whose elements, computed with the reported formulas, result as follows:

All the networks can be now connected in cascade, giving the final prototype network shown in Fig. 11. Note that the last susceptance of and the first of are modified by the element of the phase shifters. The computed response from the synthesized circuit is reported in Fig. 12 (it corresponds exactly to the one computed with the characteristic polynomials). We consider now a second example where the block is not fully canonical. To this end, the same specifications of the previous example are still used, except for the overall number of poles, which, here, is assigned equal to 8 (i.e., ). In this way, we can still use the same number of poles (two) and the same transmission zeros (imaginary) for blocks and ; the remaining four poles and two transmission zeros (real) are instead assigned to block , which, in this case, is not fully canonical any more. Two possible results of the mixed synthesis are shown in Figs. 13 and 14. In the first network (Fig. 13), is realized with a quadruplet that uses the four available nodes

synthesized as a box section

(poles); in this case, the last node of and the first node of represent the source and load of block and they are thus connected to the first and last nodes of through the inverters obtained from the synthesis of this block. Another possible prototype for the same specifications is shown in Fig. 14. In this case, the block is implemented with a box section of sixth degree (two real zeros extracted). Note that, since this block is of order 4, only four nodes are available so source and load must also be used for realizing block alone. Once is included in the final prototype, its source and load are represented by the last and first NRNs of blocks and , respectively, as depicted in Fig. 14. Fig. 15 shows the frequency response for the second example, which is exactly the same for both networks (Figs. 13 and 14). VI. EXPERIMENTAL VALIDATION An experimental validation of the method described here for the synthesis of mixed-topology filters has been carried out through a test filter for base stations of mobile communications (GSM band). The following specifications have been assumed: Band (MHz): 889.8–952.4 No. of poles: 8 Return Loss: 23 dB Transmission Zeros (MHz): 874.5, 885.2, 889.4, 889.6. The topology of the synthesized filter is shown in Fig. 16, which reports the generalized coupling coefficients [13] derived from the low-pass synthesized prototype; note that, in this particular case, Block 3 does not extract any zero. The choice of a mixed topology, even if all the zeros are imaginary, has some advantages with respect to the other topologies. In this case, in fact,

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Fig. 17. Fabricated test filter (external top view). The small circles identify the screws for tuning the cavities. Fig. 15. Frequency response of the prototypes synthesized for the second example.

Fig. 16. Topology of the de-normalized test filter. The numbers represent the resonant frequencies in megahertz (nodes) and the generalized coupling coefficient (lines); the two NRN (dashed nodes) are positive (capacitive susceptances).

a totally cross-coupled network exhibits cross-couplings with very small magnitude; as a consequence, the tuning of the zeros close to the passband would be very critical. On the other hand, with the extracted-pole configuration, there is a noticeable increase of the losses at the passband edges due to higher number of couplings between resonant and nonresonant nodes (which are structurally more complex of the couplings between resonant nodes and exhibit, as a consequence, higher losses). In conclusion, the mixed-topology represents, in this case, a good tradeoff among insertion loss, requested coupling values, and ease of tuning. The filter has been realized with coaxial cavities exhibiting an unloaded of 4000; the generalized coupling coefficients and the resonant frequencies of the cavities (reported in Fig. 16) have been obtained by de-normalizing the coupling matrix obtained with the method of Section IV (the usual lumped bandpass to low-pass transformation is used; de-normalizing equations are reported in [12]). There is a relative freedom in the choice of the susceptance slope parameter of the cavities and of the NRN susceptances; this choice must, however, take into account the physical structures implementing the cavities, the couplings (iris and probes), and the NRNs (constituted here by nonresonating stubs). In any case, a suitable use of a commercial full-wave software makes it possible to perform, in a reasonable time, the dimensioning of the whole filter. Note that tuning screws have been also included in the fabricated structure for allowing a fine tuning of the response. Fig. 17 shows a photograph of the fabricated device, while Fig. 18 reports the measured response (after a preliminary

Fig. 18. Response of the synthesized test filter. Solid lines: measured. Dashed lines: simulated (polynomial model).

tuning), compared with the simulated response (obtained from the polynomial model of the filter): the very good agreement between the curves validates the synthesis technique presented here. VII. CONCLUSION In this paper, we have described two methods for synthesizing a low-pass prototype of narrowband microwave filters with a mixed topology. The second method (the most general one) represents the filter with the cascade of three two-port blocks; the outers blocks are synthesized with extracted-pole topology, while the inner block is obtained with a cross-coupled configuration (taking into account the constraints arising when the block is fully canonical). A possible drawback of the proposed method is represented by the values of the NRN susceptances (or of the couplings), which may become relatively large in some cases (in particular, when block is fully canonical). In these cases, the physical implementation of the synthesized filter may become particularly critical. However, the synthesis methods described offer new possibilities in the selection of the filter structure to the designers of microwave filters, increasing the overall design flexibility and making it easier to find the best compromise among contrasting requirements.

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APPENDIX The de-normalized parameters of the blocks in Fig. 2 are represented by the generalized coupling coefficients [13] and the resonant frequencies . The same schematization of Fig. 2 can be used for the de-normalized network with the black nodes and the solid lines representing resonators and couplings, respectively. The following equations are obtained in the general case (source and load not involved in the scheme):

If node 1 represents the source (unit conductance), the following equations must be used:

The previous formulas can be easily modified for node 3 representing the load (unit conductance).

REFERENCES [1] A. E. Atia, A. E. Williams, and R. W. Newcomb, “Narrow-band multiple-coupled cavity synthesis,” IEEE Trans. Circuits Syst., vol. CAS-21, no. 5, pp. 469–655, Sep. 1974. [2] H. C. Bell, “Canonical asymmetric coupled-resonator filters,” IEEE Trans. Microw. Theory Techn., vol. MTT-30, no. 9, pp. 1335–1340, Sep. 1982. [3] R. Levy, “Synthesis of general asymmetric singly- and doubly- terminated cross-coupled filters,” IEEE Trans. Microw. Theory Techn., vol. 42, no. 12, pp. 2468–2471, Dec. 1994. [4] N. Yildirim, O. A. Sen, Y. Sen, M. Karaaslan, and D. Pelz, “A revision of cascade synthesis theory covering cross-coupled filters,” IEEE Trans. Microw. Theory Techn., vol. 50, no. 6, pp. 1536–1543, Jun. 2002. [5] R. Levy, “Direct synthesis of cascaded quadruplet (CQ) filters,” IEEE Trans. Microw. Theory Techn., vol. 43, no. 12, pp. 2940–2945, Dec. 1995. [6] R. J. Cameron, “Advanced filter synthesis,” IEEE Microw. Mag., vol. 12, no. 6, pp. 42–61, Oct. 2011. [7] J. D. Rhodes and R. J. Cameron, “General extracted pole synthesis mode filters,” IEEE technique with application to loaw loss Trans. Microw. Theory Techn., vol. MTT-28, no. 9, pp. 1018–1028, Sep. 1980. [8] S. Amari and U. Rosenberg, “New building blocks for modular design of elliptic and self-equalized filters,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 2, pp. 721–736, Feb. 2004. [9] S. Amari, U. Rosenberg, and J. Bornemann, “Singlets, cascaded singlets and non-resonating node model for advanced modular design of elliptic filters,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 3, pp. 237–239, Mar. 2004. [10] S. Amari and G. Macchiarella, “Synthesis of in-line filters with arbitrarily placed attenuation poles by using non-resonating nodes,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 10, pp. 3075–3081, Oct. 2005. [11] R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems. Hoboken, NJ: Wiley, 2007. [12] D. Swanson and G. Macchiarella, “Microwave filter design by synthesis and optimization,” IEEE Microw. Mag., vol. 8, no. 2, pp. 52–69, May 2007. [13] G. Macchiarella, “Generalized coupling coefficient for filters with nonresonating nodes,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 12, pp. 773–775, Dec. 2008. [14] G. Macchiarella, M. Oldoni, and S. Tamiazzo, “Design of narrowband microwave filters with mixed topology,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–4. [15] S. Amari, “Direct synthesis of cascaded singlets and triplets by nonresonating node suppression,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 12–17, 2006, pp. 111–114. [16] S. Tamiazzo and G. Macchiarella, “An analytical technique for the synthesis of cascaded -tuplets cross-coupled resonators microwave filters using matrix rotations,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 5, pp. 1693–1698, May 2005. [17] W. Stevenson, Elements of Power System Analysis. New York: McGraw-Hill, 1975.

Giuseppe Macchiarella (M’88–SM’06) is currently an Associate Professor of microwave engineering with the Department of Electronic and Information, Politecnico di Milano, Milan, Italy. He has been Scientific Coordinator of the PoliEri [a research laboratory focsued on monolithic microwave integrated circuits (MMICs)], which was jointly supported by the Politecnico di Milano and the Ericsson Company. He has authored or coauthored over 120 papers in journals and conferences proceedings. His research activity has concerned several areas of microwave engineering: microwave acoustics (surface acoustic wave (SAW) devices), radio wave propagation, numerical methods for electromagnetic, power amplifiers, linearization techniques, and passive devices. His current research activities are mainly focused on the development of new techniques for the synthesis of microwave filters.

MACCHIARELLA et al.: NARROWBAND MICROWAVE FILTERS WITH MIXED TOPOLOGY

Matteo Oldoni was born in Milan, Italy, in 1984. He received the B.Sc. degree in telecommunications engineering and M.Sc. degree from the Politecnico di Milano, Milan, Italy, in 2006 and 2009, respectively, and is currently working toward the Ph.D. degree at the Politecnico di Milano. His master’s thesis concerned the synthesis of microwave lossy filters. He is currently involved in the field of microwave filters. His research interests include synthesis and design techniques for microwave filters, algorithms development for computed-aided tuning, and improvement of numerical methods applied to electromagnetics. Mr. Oldoni was the recipient of the Young Engineers Prize of the 39th European Microwave Conference, Rome, Italy, 2009.

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Stefano Tamiazzo received the Laurea degree in telecommunication engineering from the Politecnico di Milano, Milan, Italy, in 2002, and the Master degree in information technology from Cefriel, Milan, Italy, in 2003. He is currently with Commscope, Agrate Brianza, Italy, where he is involved in the design of microwave filters and combiners for wireless applications.

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Inline Pseudoelliptic -Mode Dielectric Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Orthogonal Resonators Simone Bastioli, Member, IEEE, and Richard V. Snyder, Life Fellow, IEEE

Abstract—A new class of dielectric resonator filters with in-line structure and pseudoelliptic response is presented in this paper. single-mode resonators The basic idea consists of using cascaded along an evanescent mode waveguide and oriented along orthogonal directions. By exploiting multiple evanescent modes, which can alternatively excite or bypass a resonator depending on its orientation, cross-coupling between nonadjacent dielectric pucks can be established and controlled. Various configurations, such as triplets, quadruplets, and quintuplets, can be obtained by properly orienting the various pucks and by exploiting a prescribed set of evanescent modes. In contrast with conventional techniques, pseudoelliptic filters can be implemented without using cumbersome cross-coupled architectures or reduced spurious performance multimode resonators. The experimental results of two sixth-order filters with two arbitrarily located transmission zeros, and a fifth-order filter with three transmission zeros validate the proposed filter class. Index Terms—Bandpass filters, dielectric resonators, elliptic filters, rectangular waveguide, transmission zeros (TZs).

I. INTRODUCTION

D

IELECTRIC resonators are widely employed in modern communication systems because of their compactness and superior performance in terms of -factor and temperature stability [1]. The natural application of such a technology is within the design of very narrowband dielectric-loaded cavity filters for satellites and cellular base-stations, as well highly stable oscillators [2], [3]. Most common dielectric-loaded cavity filters employ highpermittivity disks suspended in a metallic enclosure and opermode or in the higher order ating in their fundamental mode, the latter being suitable for dual-mode operation. As the field is mainly confined within the high-permittivity dielectric puck, the ohmic losses occurring on the metallic enclosure surfaces are quite moderate. Commonly, the pucks are axially located along the metallic enclosure [4]–[7], or mounted in a planar configuration [8], [9]. dual-mode resonators allow for the realization of compact inline structures and have been extensively used for Manuscript received July 10, 2012; revised September 28, 2012; accepted September 28, 2012. Date of publication November 16, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with RS Microwave Company Inc., Butler, NJ 07405 US (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222659

satellite applications to halve the number of physical cavities of a filter structure [6], [7]. Pseudoelliptic responses can be easily obtained by realizing direct- and cross-coupling among the modes of adjacent resonators. In particular, the various modes are usually coupled so as to obtain quadruplets of resonators, thus yielding symmetric responses with an equal number of transmission zeros located below and above the passband. Dual- and triple-mode realizations of -mode dielectric resonators have been also reported in the literature [10], dual-mode resonator filters, the spu[11]. Similarly to rious performance and the design flexibility in terms of feasible cross-coupled topologies are the main limitations for these structures. Moreover, in contrast with the most common type of dielectric resonators using standard disk or ring shapes, dualand triple-mode -mode resonators result in rather complex and unconventional shapes, thus requiring a more complicated manufacturing process. single-mode cross-coupled filters with planar layout enable extended design flexibility for the realization of both symmetric and asymmetric pseudoelliptic responses [8], while providing higher spurious performance over dual-mode filters at the expense of size and mass. For these reasons, as well as their design simplicity, single-mode cross-coupled filters are probably the most used type of dielectric resonator filters, especially for terrestrial applications. Although the inline topology would be convenient for mechanical and volume occupation purposes, -mode filters with inline structure are rarely used for practical applications due to their inability to yield pseudoelliptic responses. In order to overcome the above limitation, a new configsingle-mode filter having inline structure uration of and pseudoelliptic response has been recently introduced in [12]. The basic idea consists of using dielectric pucks with two orthogonal orientations cascaded along an evanescent mode waveguide, while a pair of orthogonal evanescent modes are exploited for the generation of direct- and cross-coupling between nonadjacent pucks. Specifically, triple-resonator topologies in which a single resonator is bypassed have been proposed in [12]. This paper significantly extends the above idea by introducing additional topologies, such as quadruple- and quintuple-resonator configurations, thus leading to the definition of single-mode filters. a new class of in-line pseudoelliptic The dielectric pucks can now be oriented along all the three orthogonal directions, while an extended set of evanescent modes is exploited for the generation of cross-coupling in

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-MODE DIELECTRIC RESONATOR FILTERS TO SELECTIVELY BYPASS ORTHOGONAL RESONATORS

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TABLE I COUPLING BETWEEN WAVEGUIDE MODES AND DIELECTRIC RESONATORS

Fig. 1. Evanescent mode waveguide loaded by

-mode resonators.

which even multiple resonators can be bypassed at the same time. Compared with conventional - and –mode filters, the new class of filters maintains the convenient inline structure of the former, while having the design flexibility and spurious performance of the latter. The proposed structures can be seen as an original implementation of multimode filters in which multiple modes are used here to generate multiple paths among single-mode resonators, rather than to obtain multiple resonances within each resonator as is for the conventional multimode approaches. The concept underlying the proposed filter class is introduced in Section II. The design of triple-resonator configurations is presented in Section III, while Sections IV and V are devoted to quadruple- and quintuple-resonator configurations. The multimode coupling mechanisms occurring in all of these structures are explained and described by conventional coupling matrices, thus easing the design procedure of the otherwise complicated architectures. Section VI finally presents various experimental results that validate the new class of dielectric resonator filters. II. ORTHOGONAL RESONATORS IN EVANESCENT WAVEGUIDE The concept of exploiting propagating or evanescent modes that bypass one or more resonant modes for the realization of pseudoelliptic filters has been first proven for waveguide and coaxial cavity filters. Rectangular waveguide cavities are properly arranged so as to enable an additional input-to-output path for the electromagnetic energy carried by propagating modes [13]; single- and dual-mode cavity configurations can be found in the literature [14]–[16]. Regarding coaxial cavity filters, structures that exploit evanescent modes for the realization of cross-coupling among properly oriented nonadjacent rods have been introduced in [17]. The aforementioned principle can be extended to -mode dielectric-loaded cavity filters. This idea can be understood by considering the structure illustrated in Fig. 1, where three dielectric resonators with as many different orthogonal orientations are cascaded along an evanescent mode waveguide with a square cross section. The resonant modes of the dielectric resonators, as well as the evanescent modes of the waveguide, are indicated in Fig. 1 by means of their E-fields. In the following explanation, the coupling relationships between resonant and waveguide modes are analyzed by simple considerations on the orientation and the symmetry of the E-fields of the various modes; observe that this is an arbitrary choice,

as the same conclusions can be derived by considering the H-fields as well. The E-field of the mode resonating in the first resonator, referred to as to indicate the -axis orientation, lies on the plane. Such a field is parallel to that of the mode of the waveguide while being orthogonal with respect to the field of the mode. As a result, the mode can excite the resonator, while the mode cannot. The latter will bypass the resonant mode of the first dielectric resonator, which is seen as a simple dielectric obstacle. Opposite considerations can be applied to the second dielectric resonator, which is oriented along the -axis. The resonant mode of the second resonator can indeed be excited by the mode, being bypassed by the mode. In contrast to previous cases, neither nor modes of the third dielectric can excite the resonant mode resonator, which is located at the center of the waveguide cross section. Although the E-fields of the resonant mode and of the evanescent modes and all lie on the plane, due to symmetry reasons, no coupling occurs among has odd these modes. Specifically, the resonant mode symmetry with respect to both the - and -axes, while the modes and have even symmetry with respect to the - and -axes, respectively. These two evanescent modes will indeed bypass the third dielectric resonator, while other TE modes with odd symmetry, such as and , can excite the resonator. The three dielectric resonators are indeed isolated from each other, as none of the evanescent modes can excite more than one resonator at the same time. Observe that, although only the lowest order modes have been considered in the previous explanation, such as , the above statement holds true for all of the higher order modes of the waveguide. Table I lists all of the waveguide modes and their interaction with the three orthogonally oriented dielectric resonators: among the three sets of waveguide modes that are capable of exciting one of the resonator, the , and modes are those providing the main contribution, as the lowest order modes of each set. Only these modes will be indeed mentioned in the following to describe the interactions between waveguide and dielectric resonator modes. Coupling mechanisms among the three resonators can be established only by introducing proper waveguide discontinuities, i.e., field perturbations that generate interactions between the various waveguide modes.

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Fig. 3. Coupling mechanisms in the triple-resonator configuration. (a) Block diagram describing the multimode operation. (b) Resulting filter topology.

Fig. 2. Structure of the triple-resonator configuration: (a) parallel oriented metallic rods (TZ below the passband); (b) orthogonal oriented metallic rods (TZ above the passband).

As will be shown in the next sections, several cross-coupled topologies can be obtained by properly choosing the orientation of the resonators and by introducing useful waveguide discontinuities. III. TRIPLE-RESONATOR CONFIGURATION The triple-resonator arrangement is the simplest nonetheless useful configuration of the proposed filter class. This configuration enables the implementation of triplets, which are the basic building block for the design of pseudoelliptic filters with asymmetric response. A. Structure The structure of the triple-resonator configuration consists of a cascade of three dielectric resonators, where the inner resonator has orthogonal orientation with respect to the outer ones. Fig. 2 shows the structure of a triple-resonator configuration having outer resonators oriented along the -axis, while the inner resonator is oriented along the -axis. The mode operation occurring in the structure can be described by the block diagram shown in Fig. 3(a). The input and output probes excite the resonant mode at the first and last resonators, respectively. These outer resonators are coupled to each other by means of the evanescent mode, mode resonating in the inner reswhich bypasses the onator. Oblique metallic rods, whose orientation is typically

around 45 , are used as waveguide discontinuities between the resonators to generate a coupling between the and modes of the waveguide; in this way, part of the energy is transferred from the outer resonators to the inner resonator, the latter being excited by the mode. The resulting filter topology, commonly referred to as triplet, is diagrammed in Fig. 3(b). As is well known, such a topology generates third-order filtering functions with an asymmetric transmission zero. The transmission zero can be either located below or above the passband by inverting the phase of the field excited at the third resonator in the direct-path with respect to the phase of the bypassing mode. In practice, this is easily accomplished by moving one of the oblique rods from the bottom to the top wall of the waveguide as shown in Fig. 2(a) and (b). In the former structure of Fig. 2(a), which has parallel rods, the field from the direct path and the field of the bypassing mode are out-of-phase at the third resonator, thus generating a lower stopband transmission zero. On the other hand, in the structure of Fig. 2(b), where one of the rods is inverted with respect to the other, the resulting fields at the third resonator are in-phase, thus yielding an upper stopband transmission zero. In terms of filter topology, the out-of-phase condition of the fields in the structure of Fig. 2(a) can be equivalently described by adding a negative sign to the direct-coupling or to the bypass coupling . In all of the topologies proposed in this paper to describe the various structures, the negative sign will be arbitrarily assigned to the bypass coupling, as this is the most common usage for cross-coupled topologies. B. Coupling Control The coupling coefficients of the structure can be controlled by adjusting the distances between the resonators, as well as the dimensions of the oblique rods. With reference to Fig. 4(a), once the waveguide height is set, the distance between the outer resonators is the main parameter to control the bypass coupling . Observe that the waveguide width does not significantly affect such a coupling, as the bypass primarily occurs through the mode of the waveguide. Let us consider as an example a waveguide with 58 mm, which comprises dielectric pucks having 38-mm diameter, 20-mm height, and 35.5 relative permittivity. In this condition, the resulting resonant frequency of the resonators is around 1400 MHz, depending on the other structure dimensions.

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Fig. 6. Sequential coupling between orthogonal resonator versus 58 mm, the penetration of the 45 metallic rod: 110 mm, resonator diameter 38 mm, resonator height 20 mm, resonator dielectric permittivity 35.5, rod diameter 7.18 mm.

coupling, as a stronger interaction between the and modes is generated through the oblique rod. The coupling curves in Figs. 5 and 6 are easily derived by analyzing the resonant frequencies and of the coupled resonators in the structures of Fig. 4(a) and (b) and by applying the equation Fig. 4. Structures for computation of the coupling coefficients. (a) Bypass cou. (b) Sequenpling between outer resonators through the evanescent mode tial coupling between orthogonal resonators by using an oblique rod which creand evanescent modes. ates a coupling between the

(1) It must be noted that the introduction of the oblique metallic rods in the structure of Fig. 4(a) does not dramatically affect the bypass coupling . Although control over the coupling coefficients is not completely independent, an initial dimensioning of the structure can be carried out by first designing the distance between the outer resonators and then by adjusting the penetration of the oblique rods. In the authors’ experience, the proposed design method offers an excellent starting point for a final optimization of the whole structure, as will be shown in the following examples. C. Design Examples

Fig. 5. Bypass coupling between outer resonators versus the distance: 58 mm, resonator diameter 38 mm, resonator height 20 mm, 35.5. resonator dielectric permittivity

Fig. 5 shows the magnitude of the bypass coupling coefficient versus the distance for various dimensions of . As increases, the coupling decreases due to the decay of the evanescent mode. For the same reason, the larger the waveguide height , the stronger the coupling , as the cutoff frequency of the mode is lower. Observe that no sequential coupling and are present in the structure of Fig. 4(a). The sequential coupling coefficients and are generated by inserting oblique metallic rods among the resonators. Fig. 4(b) shows a pair of orthogonal resonator with an oblique metallic rod (45 ) inserted between them. The penetration of the rod controls the coupling coefficient. Fig. 6 shows the magnitude of the coupling versus the penetration when 58 mm: the more the penetration the stronger the

Let us consider the design of a third-order filter with center frequency 1400 MHz, fractional bandwidth 0.355%, and having a lower stopband transmission zero located at 1396.945 MHz. According to the topology of Fig. 3(b), the filtering function is described by the following normalized coupling matrix:

which can be synthesized by using standard techniques [18]–[20]. The structure of the filter implementing the above coupling matrix is the triple-resonator configuration shown in Fig. 2(a). The physical design of the structure is carried out by means of coupling curves as those reported in Figs. 5 and 6. The distance between the outer resonators is the first parameter to be dimensioned; once the distance among the resonators is set,

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Fig. 7. HFSS simulation and coupling matrix response of the designed filter in Fig. 2(a). Fig. 8. HFSS simulation and coupling matrix response of the designed filter in Fig. 2(b).

the penetration of the oblique rods can be finally designed. From the normalized coupling matrix, the coupling coefficients to be implemented in this example are and ; according to Figs. 5 and 6, the resulting structure parameters are 107 mm (by selecting 58 mm) and 22.5 mm, respectively. A final optimization of the whole structure, mainly involving a fine tuning of the resonant frequencies of the various resonators (slight adjustments on the resonators’ diameters), is eventually necessary to obtain an optimized response. Observe that, in the structure of Fig. 6, the resonant frequency of the resonators have been adjusted by The resulting dimensions after the optimization process are 109 mm and 24.2 mm, which are reasonably close to those initially estimated. The HFSS simulation of the optimized structure is shown in Fig. 7, along with the coupling matrix response: the agreement between the curves validates the filter topology used to describe the multimode operation within the structure. As previously discussed, the transmission zero can be moved to the other side of the passband by simply inverting the position of one of oblique rods as is shown in the structure of Fig. 2(b). In this condition, the magnitude of the coupling coefficients remains basically unchanged, while the bypass coupling sign is inverted. Fig. 8 shows the HFSS simulation of the optimized structure, along with the following coupling matrix response

which is the same as that of the previous filter except for the sign of the bypass coupling and of the diagonal coupling , and . IV. QUADRUPLE-RESONATOR CONFIGURATION The quadruple-resonator arrangement can be considered the basic building block for the design of symmetric elliptic filtering functions, as well as self-equalized responses.

Fig. 9. Structure of quadruple-resonator configuration. (a) Waveguide steps on opposite sides (finite frequency transmission zeros). (b) Waveguide steps on the same side (imaginary frequency zeros).

A. Structure The structure of a quadruple-resonator configuration consists of a cascade of four dielectric resonators, where the inner pair of resonators is orthogonally oriented with respect to the outer pair of resonators. Fig. 9 shows the structure of a quadruple-resonator configuration having outer resonators oriented along the -axis, while the inner resonators are oriented along the -axis. The mode operation occurring in the structure is described by the block diagram sketched in Fig. 10(a). The input and output probes excite the resonant mode at the first and last resonators, respectively. Similarly to the triple-resonator configuration, the outer resonators are coupled one to the other by mode, which bypasses the means of the evanescent resonating in the inner resonators. Two resonators are therefore bypassed at the same time in the quadruple-resonator configuration. The inner resonators, i.e., the second and third pucks, are

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Fig. 10. Coupling mechanisms in the quadruple-resonator configuration. (a) Block diagram describing the multimode operation. (b) Filter topology.

coupled one to the other by means of the evanescent and modes, which can excite the mode of the inner resonators. In contrast to the triple-mode configuration, asymmetric steps along the waveguide height are used as waveguide discontinuities between the first and the second resonators (as well as between the third and fourth ones) to generate a couand the modes of the waveguide; pling between the in this way, part of the energy is transferred from the outer resonators to the inner resonators, the latter being excited by the mode. The resulting filter topology, commonly referred to as quadruplet, is sketched in Fig. 10(b). As is well known, such a topology generates fourth-order filtering functions with a pair of symmetric transmission zero or a pair of complex frequency zeros, depending on the bypass coupling sign. In similar fashion to the triple-resonator configuration, an equivalent positive or negative sign for the bypass coupling can be obtained by inverting the phase of the field excited at the fourth resonator in the direct path with respect to the phase of the bypassing mode. In practice, this is accomplished by properly setting the relative position of the two asymmetric steps. In the structure in Fig. 9(a), where the steps are located on opposite sides of the waveguide, the resulting fields are out-of-phase at the fourth resonator, thus generating a pair of symmetric finite frequency transmission zeros (negative bypass coupling); in the structure in Fig. 9(b), where the steps are located on the same side, the resulting fields are in-phase at the fourth resonator, thus yielding imaginary frequency zeros for group delay equalization (positive bypass coupling).

Fig. 11. Structures for computation of the coupling coefficients. (a) Sequential and coupling between inner resonators through the evanescent modes . (b) Bypass coupling between outer resonators through the evanescent . (c) Sequential coupling between orthogonal resonators by using mode an asymmetric step.

Fig. 12. Sequential coupling between inner resonators versus the distance 56 mm, 155, resonator diameter 38 mm, resonator height 20 mm, resonator dielectric permittivity 35.5.

B. Coupling Control The coupling coefficients of a quadruple-resonator configuration are controlled by adjusting the distances between the resonators as well as the dimensions of the asymmetric steps. With reference to Fig. 11(a) and (b), once the waveguide dicontrols the coupling bemensions are set, the distance tween the inner pair of resonators, while the distance controls the bypass coupling between the outer pair of resonators. Fig. 12 shows the magnitude of the coupling coefficient versus the distance , while Fig. 13 shows the magnitude of the coupling coefficient versus the distance . As expected, as the distances increase, the coupling coefficients decrease due to the decay of the evanescent modes. Observe that the coupling occurs through the fundamental mode of the wave-

guide, while the coupling is mainly established by higher and modes, whose decay order modes, such as the along the waveguide is faster than that of the fundamental mode. As a result, in order to establish a useful coupling, the inner pair of resonators needs to be closer than the outer pair of resis commonly onators; for this reason the resulting distance larger than the distance , thus assuring the practical feasibility of the structure. and are impleThe sequential coupling coefficients mented through the asymmetric steps between the orthogonally oriented resonators. Fig. 11(c) shows a pair of orthogonal resonator with an asymmetric step on the bottom wall of the waveguide. Observe that the distance between the two orthogonal

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Fig. 13. Bypass coupling between outer resonators versus the distance 56 mm, 55 mm, resonator diameter 38 mm, resonator height 20 mm, resonator dielectric permittivity 35.5.

Fig. 15. HFSS simulation and coupling matrix response of the designed filter in Fig. 9(a).

0.365%, and having a pair of symmetric transmission zeros located at 1397 and 1403 MHz. According to the topology of Fig. 10(b), the filtering function is described by the following normalized coupling matrix:

Fig. 14. Sequential coupling between orthogonal resonators versus the 56 mm, 62 mm, 55 mm, step dimension 155 mm, resonator diameter 38 mm, resonator height 20 mm, resonator dielectric permittivity 35.5, step thickness 3 mm.

resonators is determined as a result of the previously designed and . The size of the steps is the design paramdistances eter that controls the coupling between the resonators. Fig. 14 versus the step dishows the magnitude of the coupling mension ; the larger , the stronger the coupling, as a stronger and modes is generated interaction between the through the step. Observe that the step thickness, whose variation would also affect the resulting coupling, is commonly set in advance, so that only the dimension is used as design parameter. In similar fashion to the oblique metallic rods discussed in Section III, the introduction of the asymmetric steps in the structure of Fig. 11(b) has only a slight effect on the bypass coupling . As a result, an initial dimensioning of the structure can be obtained by first setting the distances and then by designing the asymmetric steps. Again, similar to the triple-resonator configuration, a final optimization of the whole structure will be carried out to account for the fact that the control over the coupling coefficients is not completely independent. C. Design Examples Let us first consider the design of a fourth-order filter with 1400 MHz, fractional bandwidth center frequency

The structure of the filter implementing the above coupling matrix is the quadruple-resonator configuration shown in Fig. 9(a), where the asymmetric steps are located on opposite walls for the realization of the required negative . Similarly to the triple-resonator bypass coupling configurations, the physical design is carried out by using coupling curves as those reported in Figs. 12–14; once the distances between the resonators are set for the implementaand , the dimensions of the asymmetric steps tion of and between are sized to implement the coupling orthogonally oriented resonators. From the normalized coupling matrix, the coupling coefficients to be implemented , and in this example are ; according to Figs. 12–14, when 62 mm, the resulting structure parameters are 58 mm, 155 mm, and 5.15 mm. The HFSS simulation of the optimized structure is shown in Fig. 15, along with the corresponding coupling matrix response. As for the triple-resonator configuration, the agreement between the curves validates the filter topology that we are using to describe the multimode operation within the quadruple-resonator configuration. As a second example, let us consider the design of a self-equalized fourth-order filter with center frequency 1400 MHz and fractional bandwidth %, whose

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Fig. 17. Structure of the quintuple-resonator configuration. (a) Waveguide steps on the opposite sides (two TZs below and one TZ above the passband). (b) Waveguide steps on the same side (two TZs above and one TZ below the passband).

V. QUINTUPLE-RESONATOR CONFIGURATION In contrast with the triple- and quadruple-resonator configurations, the quintuple-resonator arrangement employs all three orientations for its resonators, as well as three main waveguide evanescent modes. This configuration yields asymmetric filtering functions with five poles and three transmission zeros. A. Structure

Fig. 16. HFSS simulation and coupling matrix response of the designed filter in Fig. 9(b). (a) -parameters. (b) Passband group delay.

filtering function is described by the following normalized coupling matrix:

The structure of the filter implementing the above coupling matrix is the quadruple-resonator configuration shown in Fig. 9(b), where the asymmetric steps are located on the same wall, thus realizing required positive bypass coupling . Fig. 16(a) shows the HFSS simulation of the filter along with the coupling matrix response, while Fig. 16(b) shows the corresponding group delay. The filter structure has been designed by following the same procedure as before, and the resulting struc58 mm, ture parameters of the optimized filter are 59 mm, 156 mm, and 9.05 mm.

The structure of a quintuple-resonator configuration consists of a cascade of five dielectric resonators, as shown in Fig. 17. The first and fifth resonators are oriented along the -axis, while the second and fourth resonators are oriented along the -axis. Finally, the third resonator, which is the inmost one, is oriented along the -axis. The mode operation occurring in the structure is described by the block diagram sketched in Fig. 18(a). The input and output probes excite the resonant mode at the first and fifth resonators, respectively. These outer resonators are coupled one to the other by means of the evanescent mode, which bypasses the and resonating in the inner resonators. Three resonators are therefore bypassed at the same time in this configuration. The second and fourth resonators are coupled one to the other by means of the evanescent , which bypasses mode of the third resonator. The first and second resthe onators, as well as the fourth and fifth resonators, are coupled to each other by means of oblique metallic rods, which generate an interaction between the and modes. The third resonator is coupled to the second and fourth resonators by means of asymmetric steps, which generate an interaction between the and modes. The resulting filter topology is sketched in Fig. 18(b). Such a topology can generate 5th order filtering functions with three transmission zeros. Depending on the signs of the two bypass coupling, two transmission zeros can be located on one side of of the passband, while the third transmission zero will be located on the opposite side.

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Fig. 18. Coupling mechanisms in a quintuple-resonator configuration. (a) Block diagram describing the multimode operation. (b) Resulting filter topology.

As for the previous structures, the relative position of the oblique rods, as well as the relative position of the two asymmetric steps with respect to each other, determines the signs of the bypass coupling. Among the various possibilities, two convenient locations for rods and steps are shown in the structures of Fig. 17. The structure in Fig. 17(a) yields a negative sign for the bypass coupling while giving a positive sign for the bypass coupling . As a result, two transmission zeros are located below the passband, while one transmission zero is located above the passband. On the other hand, the structure in Fig. 17(b), in which the two asymmetric steps are realized on the same side of the waveguide, yields a positive sign for the bypass coupling while giving a negative sign for the bypass coupling . In the latter case, two transmission zeros will be located above the passband while one transmission zero will be located below the passband. B. Coupling Control As for the previous structures, the coupling coefficients of a quintuple-resonator configuration are controlled by adjusting the distances between the resonators as well as the dimensions of the oblique metallic rods and of the asymmetric steps. With reference to Fig. 19, once the waveguide width and height are set, the distance is the main parameter to control the bypass coupling , while the distance controls the bypass coupling . The waveguide width mainly affects the coupling , as this bypass primarily occurs through the mode, while the waveguide height mainly affects the coupling , the latter occurring through the mode.

Fig. 19. Bypass coupling mechanisms. (a) Bypass coupling between second and fourth resonators through the mode. (b) Bypass coupling between outer resonators through the mode.

The sequential coupling coefficients are controlled in the same way as done for the previous configurations: the oblique metallic rods affect the coupling and , while the asymmetric step dimensions affect the coupling and . The implementation of the coupling coefficients can be carried out by deriving and analyzing coupling curves similar to those reported in the previous sections for the triple- and quadruple-resonator configurations. C. Design Examples Let us consider the design of a fifth-order filter with center frequency 2174 MHz, fractional bandwidth 0.66%, and having three transmission zeros located at 2160.3, 2164.8, and 2192 MHz. According to the topology of Fig. 18(b), the filtering function is described by the normalized coupling matrix shown at the bottom of this page. The structure of the filter implementing the above coupling is the quintuple-resonator configuration shown in Fig. 17(a). The agreement between the HFSS simulation of the optimized structure and the coupling matrix response is shown in Fig. 20, thus validating the topology we are using for the description of the quintuple-resonator configuration. As was previously discussed, the transmission zeros can be inverted with respect to the passband by simply changing the position of one of the asymmetric steps, as shown in the structure of Fig. 17(b). The simulations and the experimental results of a manufactured prototype based on the structure of Fig. 17(b) are reported in Section VI.

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Fig. 20. HFSS simulation and coupling matrix response of the designed filter in Fig. 17(a).

Fig. 21. Sixth-order filter made out of two cascaded triple-resonator configurations. (a) Structure. (b) Topology.

VI. EXPERIMENTAL RESULTS A. Cascaded Triple-Resonator Configurations A sixth-order filter made out of two cascaded triple-resonator configurations has been designed and manufactured. The filter structure and its topology are shown in Fig. 21. Observe that the two triplets are cascaded by means of an iris, which is inductive with respect to the mode. Besides controlling the sequential coupling between the third and fourth resonators, such an inductive iris is essential to suppress the evanescent mode, thus preventing the presence of an unwanted bypass coupling

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Fig. 22. Manufactured sixth-order filters. (a) Ssymmetric response filter with two transmission zeros below the passband. (b) Symmetric response filter with two symmetrically located transmission zeros.

between the second and the fifth resonators (which both are oriented along the -axis). Each triple-resonator configuration is responsible for the generation of a transmission zero, which can be arbitrarily located below or above the passband. In particular, due to the parallel orientation of the oblique metallic rods in each triplet, the structure of Fig. 21 gives two transmission zeros below the passband. The designed filter has 20-dB return loss passband between 2164 and 2176 MHz, and its response has been optimized according to the normalized coupling matrix shown at the bottom of this page ( 2170.15 MHz, 0.576%), which yields two transmission zeros at 2161.98 and 2163.06 MHz, respectively. Observe that the transmission zeros are very close to the lower cutoff frequency of the passband (about 2 MHz and less than 1 MHz distant). A photograph of the interior of the manufactured prototype is shown in Fig. 22(a). High-permittivity (77) dielectric pucks with a -factor of 5000 are used for this design. Low-permittivity dielectric supports hold in place the dielectric resonators. Besides the oblique metallic rods that are used for coupling purposes, an additional metallic rod is used for each of the resonators in order to tune their resonant frequencies. Observe that the presence of these additional rods must be taken into account in the HFSS model for an accurate simulation and optimization of the structure.

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Fig. 23. Structure parameters of the sixth-order filter with asymmetric response: tuning rods on the resonators are included in the structure, which employs six identical dielectric pucks with 77 dielectric permittivity. All of the metallic rods have 6.35-mm diameter.

TABLE II DIMENSIONS OF THE SIXTH-ORDER FILTER WITH ASYMMETRIC RESPONSE

Fig. 24. Measured -parameters, HFSS simulation (lossless), and coupling matrix response of the sixth-order filter of Fig. 22(a).

Fig. 25. Broadband measurement of the sixth-order filter of Fig. 22(a).

With reference to Fig. 23, the dimensions of the manufactured prototype are delineated in Table II. The measured -parameters are shown in Fig. 24 along with the lossless HFSS simulation and coupling matrix response: the agreement between the curves validates the model that we are using to describe the multimode operation within the filter. The measured insertion loss at the filter center frequency is 1.45 dB, thus corresponding to an experimental -factor of around 3700. The spurious-free stopband is shown in Fig. 25: it extends up to 2.75 GHz, which is about 1.27 times the filter center frequency, as is common for disk-shaped -mode resonator filters. Finally, the temperature test results are shown in Fig. 26. Besides a 350-kHz frequency shift (which is in agreement with the physical characteristics of the particular dielectric resonators used in this filter), the relative positions of poles and zeros do not significantly change over temperature. These results demonstrate that the resonant frequencies of the differently oriented resonators move uniformly over temperature, and it reveals that the bypass coupling is temperature stable. The latter finding is mainly due to the fact that the bypass coupling is established by evanescent nonresonating modes, which are commonly less sensitive compared with resonating modes.

Fig. 26. Temperature test results of the sixth-order filter of Fig. 22(a).

Let us consider another filter example in which the two transmission zeros are symmetrically located with respect to the passband. The filter structure is the same as that of the previous filter, except for the fact that the orientation of the first oblique metallic rod in the first triplet is inverted. A photograph of the prototype with the inverted rod is reported in Fig. 22(b). The filter has been tuned so as to obtain 18-dB return loss passband between 2164 and 2179 MHz. The

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Fig. 28. Manufactured fifth-order filter.

Fig. 27. Measured -parameters, HFSS simulation (lossless), and coupling matrix response of the sixth-order filter of Fig. 22(b).

filter response can be described by the normalized coupling matrix shown at the bottom of this page ( 2171.65 MHz, 0.705%), which yields two transmission zeros at 2161.98 and 2163.06 MHz, respectively. The agreement between the measured -parameters and the ideal lossless coupling matrix response is shown in Fig. 27. The measured insertion loss at the filter center frequency is 1.15 dB, thus corresponding again to an experimental -factor of 3700. The latter design example demonstrates the high design flexibility of the proposed filter class in the transmission zero positioning. B. Quintuple-Resonator Configuration A fifth-order filter based on the quintuple-resonator structure of Fig. 17(b) has been designed and manufactured. The filter center frequency is 2140 MHz, while the fractional bandwidth is 1%. The filter response has been optimized according to the normalized coupling matrix shown at the bottom

of this page, which yields three transmission zeros at 2117, 2153, and 2158 MHz, respectively. As 1% fractional bandwidth is commonly considered the upper limit for dielectricloaded cavity filters, this design example demonstrates that the proposed filter class is also suitable for the realization of relatively wideband filters, thus proving the absence of significant limitations in the implementation of relatively strong coupling coefficients. A photograph of the interior of the manufactured prototype is shown in Fig. 28. As for the previous designs, the same highpermittivity (77) dielectric pucks with a -factor of 5000 are employed in this unit. The measured -parameters are shown in Fig. 29 along with the lossless HFSS simulation and coupling matrix response. The measured insertion loss at the filter center frequency is 0.75 dB, which corresponds once again to an experimental -factor of about 3700. For all three experimental results, the measured -factor is therefore close to 75% of the -factor of the dielectric pucks (ideally considered without any metallic enclosure): this result is in agreement with our expectation considering the proximity of the waveguide walls, the low

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or reduced spurious performance dual-mode resonators. The experimental results of some manufactured prototypes, such as two 6th order filters made out of cascaded triplets and a fifth-order filter consisting of a quintuple-resonator configuration, have been presented to validate the proposed filter class. It is worth noting that different shapes, as well as a different mode operation for the resonators, are possible to improve or optimize the filter performance with respect to prescribed requirements: as an example, the spurious performance of the proposed filter class can be improved by using ring-shaped resonators, instead of disk-shaped resonators, as is commonly done for other conventional single-mode dielectric loaded-cavity filters. Fig. 29. Measured S –parameters, HFSS simulation (lossless), and coupling matrix response of the fifth-order filter of Fig. 28.

permittivity dielectric supports, as well as the tuning rods on the resonators. Although the latter measurement validates the feasibility of the quintuple-resonator configuration, in contrast with the previous experimental results, a slight discrepancy between simulations and measurement is observed in Fig. 29. Part of such a deviation must be ascribed to the simulated model: in contrast with the previous designs, no low-permittivity dielectric supports and tuning rods have been considered in the HFSS model of this structure. In particular, it has been verified that a relatively long tuning rod does have an effect on those bypassing modes whose polarization is parallel with the rod, thus altering the resulting bypass coupling coefficients. The latter fact suggests that the tuning rods should be kept as short as possible and/or be included in the design model. Another reason to justify the deviation between simulation and measurements is the presence of unwanted coupling between the resonators, in particular between the outer resonators and the third resonator, whose assembly ( -axis orientation) is a bit more complex than the others. Specifically, such a resonator is supposed to be accurately centered with respect to the waveguide cross section in order to avoid the generation of spurious coupling with the outer resonators of the filter. More attention to all of these details will be given for the design and manufacturing of future units. VII. CONCLUSION A new class of dielectric resonator filters with inline structure and pseudoelliptic response has been presented in this paper. The basic idea consists of using single-mode resonators oriented along orthogonal directions in combination with multiple waveguide evanescent modes, which provide multiple paths for the EM energy transferred among the various resonators. In this way, cross-coupling between nonadjacent resonators can be established. Various configurations for the realization of asymmetric and symmetric pseudoelliptic responses, as well as self-equalized filters, have been proposed. In contrast with conventional techniques, pseudoelliptic and self-equalized filters can be implemented within an inline structure without using cumbersome cross-coupled architectures,

REFERENCES [1] C. Wang and K. A. Zaki, “Dielectric resonators and filters,” IEEE Microw. Mag., vol. 8, no. 5, pp. 115–127, Nov. 2007. [2] S. J. Fiedziuszko and S. Holmes, “Dielectric resonators raise your high-Q,” IEEE Microw. Mag., vol. 2, no. 3, pp. 50–60, Sep. 2001. [3] R. R. Mansour, “Filter technologies for wireless base stations,” IEEE Microw. Mag., vol. 5, no. 1, pp. 68–74, Mar. 2004. [4] S. B. Cohn, “Microwave bandpass filters containing high-Q dielectric resonators,” IEEE Trans. Microw. Theory Tech., vol. MTT-16, no. 4, pp. 218–227, Apr. 1968. [5] W. H. Harrison, “A miniature high-Q bandpass filter employing dielectric resonators,” IEEE Trans. Microw. Theory Tech., vol. MTT-16, no. 4, pp. 210–218, Apr. 1968. [6] S. J. Fiedziuszko, “Dual-mode dielectric loaded cavity filters,” IEEE Trans. Microw. Theory Tech., vol. MTT-30, no. 9, pp. 1311–1316, Sep. 1982. [7] K. A. Zaki, C. Chen, and A. E. Atia, “Canonical and longitudinal dual mode dielectric resonator filters without iris,” IEEE Trans. Microw. Theory Tech., vol. MTT-35, pp. 1130–1135, Dec. 1987. [8] J.-F. Liang and W. D. Blair, “High-Q TE01 mode DR filters for PCS wireless base stations,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2493–2500, Dec. 1998. [9] H. Rafi, R. Levy, and K. Zaki, “Synthesis and design of cascaded trisection (CT) dielectric resonator filters,” in Proc. 27th Eur. Microw. Conf., 1997, vol. 2, pp. 784–791. [10] D. D. Fernando, I. C. Hunter, and V. Postoyalko, “Dual-mode dielectric resonator,” in Proc. 29th Eur. Microw. Conf., 1999, vol. 3, pp. 51–54. [11] Y. Ishikawa, T. Wada, H. Nishida, and S. Hidaka, “TE101 Triple Mode Dielectric Resonator Apparatus,” U.S. Patent 5 325 077, Jun. 28, 1994. mode di[12] S. Bastioli and R. V. Snyder, “In-line pseudoelliptic electric resonator filters,” in IEEE MTT-S. Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [13] S. Bastioli, “Nonresonating mode waveguide filters,” IEEE Microw. Mag., vol. 12, no. 6, pp. 77–86, Oct. 2011. -mode fil[14] U. Rosenberg, S. Amari, and J. Bornemann, “Inline ters with high design flexibility by utilizing bypass couplings of nonmodes,” IEEE Trans. Microw. Theory Tech., vol. resonating 51, no. 6, pp. 1735–1742, Jun. 2003. [15] S. Bastioli, C. Tomassoni, and R. Sorrentino, “A new class of waveguide dual-mode filters using TM and nonresonating modes,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 12, pp. 3909–3917, Dec. 2010. [16] C. Tomassoni, S. Bastioli, and R. Sorrentino, “Generalized TM dualmode cavity filters,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 12, pp. 3338–3346, Dec. 2011. [17] Y. Wang and M. Yu, “True inline cross-coupled coaxial filters,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 12, pp. 2958–2965, Dec. 2009. [18] A. E. Atia and A. E. Williams, “Narrow-bandpass waveguide filters,” IEEE Trans. Microw. Theory Tech., vol. 20, pp. 258–265, Apr. 1972. [19] R. J. Cameron, “Advanced coupling matrix synthesis techniques for microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 1–10, Jan. 2003. [20] S. Amari, U. Rosenberg, and J. Bornemann, “Adaptive synthesis and design of resonator filters with source/load-multiresonator coupling,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 8, pp. 1969–1978, Aug. 2002.

BASTIOLI AND SNYDER: PSEUDOELLIPTIC

-MODE DIELECTRIC RESONATOR FILTERS TO SELECTIVELY BYPASS ORTHOGONAL RESONATORS

Simone Bastioli (S’10–M’11) received the M.S. and Ph.D. degrees in electronic engineering from the University of Perugia, Perugia, Italy, in 2006 and 2010, respectively. In 2005, he was an Intern with Ericsson AB, Mölndal, Sweden, working on waveguide filters and transitions for radio frequency applications. In 2006, he was admitted as Ph.D. student at University of Perugia with a scholarship funded by the Italian Space Agency (ASI). In 2009, he was with RF Microtech Srl, Perugia, Italy, where he was responsible for the design of advanced microwave filters for private and European Space Agency (ESA) funded projects. In 2010, he joined RS Microwave Company Inc., Butler, NJ, where he is currently a Senior Microwave Research Engineer working on reduced size multimode cavity filters, advanced high-power evanescent-mode filters, as well as dielectric resonator and lumped-element filters. Dr. Bastioli is a member of MTT-8 Filters and Passive Components Technical Committee. He was the recipient of the 2012 IEEE Microwave Prize. In 2008, he was awarded with the Best Student Paper Award (First Place) at the IEEE MTT-S International Microwave Symposium (IMS) held in Atlanta, GA, USA, and with the Young Engineers Prize at the European Microwave Conference held in Amsterdam, The Netherlands. In 2009, he was the recipient of the Hal Sobol Travel Grant presented at the IEEE MTT-S IMS held in Boston, MA, USA. His research activities resulted in more than twenty publications in international journals and conferences, as well as four patent applications.

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Richard V. Snyder (F’97–LF’05) received the B.S. degree from Loyola Marymount University, Los Angeles, CA, the M.S. degree from the University of Southern California, Los Angeles, and the Ph.D. degree from Polytechnic Institute of New York, Brooklyn. He is President of RS Microwave Company Inc., Butler, NJ, author of 84 papers and three book chapters, and holds 19 patents. He is a Visiting Professor with the University of Leeds, Leeds, U.K. He previously was Chief Engineer for Premier Microwave. His interests include E-M simulation, network synthesis, dielectric and suspended resonators, high power notch and bandpass filters and active filters. he teaches and advises at the New Jersey Institute of Technology. Dr. Snyder is a member of the American Physical Society, the AAAS and the New York Academy of Science. He served the IEEE North Jersey Section as Chairman and 14 year Chair of the Microwave Theory and Techniques (MTT)Antennas and Propagation (AP) chapter. He chaired the IEEE North Jersey EDS and CAS chapters for 10 years. He twice received the Region 1 award. In January 2000, he received the IEEE Millennium Medal. He served as General Chairman for IMS2003, in Philadelphia. He was elected to ADCOM in 2004. Within the ADCOM, he served as Chair of the TCC and Liaison to the EuMA. He served as an IEEE Microwave Theory and Techniques Society (MTT-S) Distinguished Lecturer, from 2007 to 2010, as well as continuing as a member of the Speakers Bureau. He was an associate editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, responsible for most of the filter papers submitted. He was the MTT-S President for 2011. Also a reviewer for IEEE MTT publications and the MWJ, he served seven years as Chair of MTT-8 and continues in MTT-8/TPC work.

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A

-Band Fully Tunable Cavity Filter Bahram Yassini, Member, IEEE, Ming Yu, Fellow, IEEE, and Brian Keats

Abstract—A TE -band tunable filter with a stable and continuous tuning performance is presented in this paper. Both bandwidth and center-frequency tunability are demonstrated by cascading six-pole pseudo-low-pass and pseudo-high-pass tunable filters. A novel mode-splitter resonator and coupling configuration enabling cross-coupled planar TE filter realization is introduced in this paper. The concept can be applied to back-toresonators as well. The filter design is verified back coupled TE through fabrication of multiple tunable filters that demonstrates 500 MHz of tuning range with a stable RF tuning performance. Index Terms—Cavity resonators, coupling, reconfigurable architectures, TE , tunable filters.

I. INTRODUCTION

R

EALIZING a flexible transceiver, particularly for reconfigurable payloads, presents a number of technical challenges; bandwidth tunability, center-frequency tunability, and selectivity must be achieved over a wide frequency range [1]. If tunability is realized by resizing cavities, the actuation system must exhibit minimal power consumption. Latching is required to ensure that power is only consumed during a tuning operation and to maintain filter performance while the mechanism is unpowered. A key design parameter in realizing the filter function for a tunable filter is the desired mode. The field pattern of a cylindrical cavity operating in the TE mode is an attractive choice for tunable filters. Along with a high quality factor, the field pattern and current distribution offer key advantages for realizing tunable filters. However, this mode of operation is degenerate with a pair of low-qualityfactor TM modes that need to be separated from the operating TE mode without degrading the quality factor or overall filter performance [2], [3]. Realization of a filter function in a cross-coupled resonator configuration such as this presents another challenge [4]; however, a cross-coupled realization is essential since a planar layout allows for a single actuation mechanism to realize tunability. To the best of our knowledge, no demonstration of stable tuning performance using this mode can be found in the literature. The most efficient technique to split the degenerate TM mode from the operating TE mode is shaping the cavity resonator [2], [3]. This technique uses a barrel-shaped cavity reManuscript received July 10, 2012; revised September 19, 2012; accepted September 24, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported by the Canadian Space Agency (CSA). This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17-22, 2012. The authors are with COM DEV Ltd., Cambridge, ON, Canada N1R 7H6 (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2224367

lating the modes of a cylindrical cavity to those of a spherical cavity. However, this shaping method increases the overall filter footprint and is difficult to manufacture. Another technique introduced in [4] employs metallic posts to split the degenerate TM mode, but it suffers from fabrication complexity and performance degradation. In [5], a disc-loaded technique is presented for the -band. The efficacy of this technique is not substantiated and clarified. In [5], however, the disc is not used to split the degenerate TM mode. All of the published TE filters use a below-resonance iris (short iris) to couple two cavities. This type of iris only realizes one coupling sign in a side-to-side (planar) cross-coupled cavity configuration. Therefore, it does not offer an all-purpose and comprehensive solution to realize any desired filter function in a planar and cross-coupled fashion using TE cavity resonator. Although the extracted-pole technique [6] can be employed to realize a filter response in a planar fashion using the same sign coupling configuration, this technique suffers from a size disadvantage. The extracted pole design is not attractive for tunable filter design because of the frequency-sensitive transmission lines used between cavities. The back-to-back coupling employing an offset-cavity technique in two layers described in [4] can provide both positive and negative couplings. This method increases the overall filter envelope due to the offset cavity configuration. This configuration is not practical where a single actuation mechanism will simultaneously tune all cavities. The single-layer cross-coupled cavity design presented in this paper is an attractive filter configuration, particularly for tunable filter realization. This configuration requires both positive and negative coupling to realize the desired filter function. A design that can address both coupling signs in a planar cross-coupled fashion has not been introduced in the literature. The presented tunable filter technology offers both bandwidth and center-frequency tunability. By matching the tuning curves of the cavities, a single actuation mechanism can be used for all filter cavities. This configuration minimizes power consumption and complexity. II. END-CAP METAL-RING TM

MODE-SPLITTER

mode, a feature is reIn order to split the degenerate TM resonance, while minimally quired that will move the TM affecting the desired TE011 mode. Electromagnetic field and current distribution for the desired and the high-frequency spurious TE , the degenerate TM modes are shown in Fig. 1. Normalized electric field TE strength versus normalized radius for all of the electric field components of these modes are also shown in Fig. 2. TE -mode electric field strength and current distribution approach zero at both the center and edge of the cavity. Due

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Fig. 1. Electric and magnetic field and current distribution for the TE modes. TM , and TE

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,

Fig. 2. Normalized electric field strength versus normalized radius.

to the weakness of the current flow and electric field at the center and edge of the end walls, introducing a properly designed perimeter channel and center bore as shown in Fig. 3 will have a minimal effect on the desired TE mode. However, the TM -mode current distribution is strong at both the center and edge of the end wall. Both radial and angular components of the electric field are strong at the center while the radial component is also strong at the perimeter. Although the longitudinal component of this mode follows the same distribution versus cavity radius as the angular component of the TE electric field, it has the opposite distribution along resonator axis and has its maximum at the end wall. The perimeter channel and center bore described in Fig. 3 will therefore perturb this mode strongly and lower the resonant frequency significantly. The magnitude of this shift depends on the dimensions of the channel and bore. The bore diameter should be less than 48% of cavity diameter since longitudinal electric field of TM is maximum at this point, and the bore will counter-affect the gap if it is larger than that value. The high-frequency spurious TE mode is strong at the end-wall edge and weak at the center. Its resonant frequency

is also shifted lower by the end cap channel and bore. However, the impact is significantly less than on the TM mode due to the longitudinal electric component of the TM mode being maximum at the end cap. The impact is also lessened by the differing field and current distribution (Fig. 1). The channel and bore dimensions should be carefully designed to optimize the spurious-free window with the minimum impact on the TE quality factor or exciting other unwanted modes. The structural details of the mode-splitting end cap are shown in Fig. 3. The combination of the perimeter channel and center bore forms an end-cap metal ring mode-splitter. The cavity can be loaded with one or two mode-splitters, depending on the application. The channel can cause unwanted resonance if the length is too close to a quarter-wavelength (of free space). The channel length must therefore be well below a quarter wavelength to avoid these unwanted resonant frequencies. A movable end cap can be introduced in the cavity to make it tunable, as shown in the Fig. 3. Electrical contact must be provided between the end of the channel and the cavity wall. The enclosure contact must provide adequate conductivity to create a near short-circuit condition. This will guarantee that the degenerate TM mode and other spurious modes are kept outside of the operating frequency range. This criterion can also be achieved with reactive impedance. Violating this condition may provide unwanted surface impedance that will not only shift the TE and TM mode undesirably, but also create other unwanted resonant modes that can be sufficiently close to the operating frequency to degrade the overall filter performance. It is well known that the imperfect conductivity at the enclosure contact does not affect the quality factor of the operating TE mode. Therefore, the enclosure criteria can be met with a sliding contact mechanism to create tunability for a resonator or filter. The spurious performance of the proposed resonator is shown in Fig. 4. A resonator without the center bore is shown for comparison. The channel length is varied from 0.05 to 0.09 in and TE , TM , and TE resonant frequencies are computed using a full-wave solver. More than 2 GHz of spurious-free window (TE -TM ) is achieved using this technique. The figure shows that the center bore shifts the degenerate TM mode further toward lower frequencies without impacting TE and TE modes. For the dimensions shown here, end caps with both a perimeter channel and center bore increase the spurious-free window by 400 MHz compared with a perimeter channel alone. III. LONG IRIS FOR POSITIVE COUPLING A coupled TE resonator is shown in Fig. 5. Coupling is realized through an iris. It is common practice to use an iris with a length less than half the free-space wavelength (below resonance). This type of iris is referred to here as a short iris. A short iris provides only negative coupling. Introducing an iris with positive coupling offers additional design flexibility, since it allows for a filter layout with both

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Fig. 3. Tunable TE

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resonator with mode-splitter rings.

coupling signs. An iris with a length longer than half of the free-space wavelength (over the resonance) can provide positive coupling (opposite sign of the short iris) between cavities. This configuration is referred to here as a long iris. The following is an example on how these two irises are different. Table I shows the simulated odd- and even-mode frequencies for short and long irises in a side-to-side metal ring loaded TE coupled resonators. It has to be noted that cavities should be properly sized to fit the long iris without performance degradation. It is clear from this table that the coupling sign of the long iris is opposite of the one for the short iris. The idea of the long iris is also applicable to the back-to-back coupled resonator. One interesting characteristic of the long iris is its low sensitivity to its height variation and to the cavity length (cavity resonant frequency) change. This feature makes it a good candidate for applications that require stable coupling over a wide frequency range or cavity-length variation. Consider a block of tunable resonator, as shown in two coupled side-by-side TE Fig. 5. The top end walls of both cavities include metal rings displaced by 0.02 in to represent more than 450-MHz range at -band (20 GHz). Coupling variation for short and long irises is shown in Fig. 6. This figure shows that the long iris coupling value variation is less than 3.5% versus 10% for the short iris over more than 450 MHz (around 2.5%) of tuning range. Therefore, tunable filters with a stable response can be designed by incorporating long irises in the design.

IV. APPLICATION IN FILTER DESIGN The introduction of a long iris offering positive coupling (along with a short iris with negative coupling) can be employed to improve the TE011 filter design for both functionality and layout. Realizing many filter functions in a cross-coupled planar TE011 structure is feasible by employing long and short irises properly. A. A Four-Pole Elliptic Filter Function Both coupling signs are required to realize a cross-coupled four-pole elliptical filter function with two transmission zeros. Long and short irises can be used to realize such a filter in a planar TE configuration, as shown in Fig. 7. The filter structure comprises of three sequentially coupled long irises (positive signs) and one short iris to realize negative cross coupling. Resonators are loaded metal-ring mode splitters to isolate the TM mode. Input and output ports are rotated by 30 to minimize stray coupling and balance the notches. Full-wave simulation of such a filter is shown in Fig. 8. The in-band response is clean, and the degenerate mode is shifted down as expected. Simulation demonstrates that the degenerate TM mode is lowered by another 450 MHz by the center bore as expected. B. Realizing Planar Asymmetric Filter Functions Asymmetric filter functions can be realized using trisection building blocks as shown in Fig. 9. Trisection building blocks

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TABLE I BOTH COUPLING SIGNS FOR A DIRECT COUPLED TE

CAVITIES

shown in Fig. 9(a) and (b), respectively. These are six-pole filters with two transmission zeros. Each trisection provides three poles and one transmission zero. Although both pseudo-low-pass and pseudo-high-pass coupling matrices are not unique, one can conclude that the pseudo-low-pass version is not realizable without positive coupling [7]. The positive-coupling long iris is used to realize this filter. A cross-coupled pseudo-low-pass filter employing all positive coupling signs is shown in Fig. 9(a). This filter function is realizable in a planar TE direct-coupled configuration using the introduced long iris [8]. Fig. 10 shows a layout of such a filter incorporating two trisections and cavities loaded with a metal-ring mode splitter. All of the TE resonator cavities are directly coupled using long irises to realize positive coupling. The same layout with different iris sizes can be used for pseudo-high-pass versions to realize the coupling structure shown in Fig. 9(b). A pseudo-high-pass filter is also realizable using all negative coupling signs. V. TUNABLE TE Fig. 4. Spurious modes for a 20-GHz TE resonator with metal ring 0.51 mm, bore diameter 6.35 mm, mode-splitter. Channel width 22.23 mm, and resonator length 13.18 mm. (a) TE cavity diameter and the closest spurious modes. (b) Spurious-free window.

Fig. 5. Two TE metal ring-loaded resonators coupled through an iris. (a) Side view. (b) Top view.

offer size and expandability advantages. Coupling structure for both pseudo-low-pass and pseudo-high-pass 6-2 filters are

FILTER

A variety of tunable filter technologies have been reported in literature and industry [9]–[21]. Presenting both bandwidth and center frequency tunability with a stable response over a wide tuning range is still a major challenge among them. It is known that bandwidth adjustment can be realized by cascading two (low-pass and high-pass) tunable filters. Both bandwidth and center frequency can then be tuned by tuning each filter center frequency with respect to each other. The resultant cascaded performance is the overlap of the two filter responses. Both filters should maintain their in-band and rejection performance when tuning center frequency. This is the main challenge in the cascade approach, particularly at microwave frequencies. The introduced tunable metal-ring loaded TE cavity and long coupling iris (positive coupling) are the key elements to realize such a stable tunable filter response. TE metal-ring loaded cavity resonators and combinations of long and short irises can be employed to realize both pseudolow-pass and pseudo-high-pass filters in the same planar layout, as shown in Fig. 10. The center bore of the metal ring is not used for simplicity in the example provided in this paper. The center bore can be added if a wider spurious-free window is required.

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Fig. 7. Four-pole planar TE filter incorporating mode-spliter ring and long and short irises to realize elliptic filter function.

coupling irises (Iris-12 and Iris-56, respectively) to suppress TE coupling and reduce stray coupling. Each cavity has a different resonant frequency, as shown by coupling matrices in Fig. 9(a) and (b). Therefore, tuning curves of cavities must match each other to maintain filter response over the tuning range. Independent cavity actuation can achieve that at the cost of multiple actuation systems and a more complex tuning mechanism. A single actuation mechanism is possible if the tuning curves are matched for each cavity. The resonant frequency of each TE cavity is governed by the following equation:

(1)

Fig. 6. Coupling value variation for a -band (20 GHz) metal ring-loaded coupled resonators. (a) Coupling variation versus displacement (b) CouTE pling variation versus resonance frequency.

It is important where possible to use (long) positive coupling irises in both designs to achieve a stable RF performance over the tuning range as the long iris exhibits a very small coupling variation over the tuning range (Fig. 6). Therefore, the pseudo-low-pass filter is realized using all positive (long) coupling irises. The pseudo-high-pass version is realized using five positive (long) coupling irises for sequential coupling and two negative (short) coupling irises for cross coupling. Input and output irises are located at 90 with respect to the sequential

is the first zero of the derivative of the Bessel function where of the first kind and order 0 and and are length and radius of the th cavity, respectively. The derivative of resonant frequency of each cavity with respect to its length can be derived from (1) as (2) Therefore, the following criterion ensures that resonator tuning curves matches at the middle of the tuning range: (3) Considering the typical dimensions of a -band (20 GHz) TE filter (Fig. 4) and (2), the tuning slope is in the range of

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Fig. 10. Cross-coupled planar TE filter layout incorporating metal-ring mode-splitter and long/short irises to realize both pseudo-low-pass and pseudo-high-pass 6-2 filter functions.

Fig. 11. Tunable filter moving section including tuning plate, tuning disc/plunger, and sliding contact. Fig. 8. Simulated response of a four-pole planar TE elliptic filter. The design with (blue) and without (red) center bore shows that the center bore helps mode by 450 MHz without affecting TE spurious. to further split the TM (a) Transmission response. (b) Return loss.

10 MHz/mil. Thus, 25 mil ( of cavity length) is required for 250-MHz (a total of 500 MHz) tuning range. Bearing in mind the self-coupling values presented in the coupling structure from Fig. 9, a bandwidth of 170 MHz, and a tuning range of 500 MHz, one can use the first-order approximation of (3) and derive the following formula for the length of each cavity with respect to the length of first resonator or any desired reference resonator: (4)

Fig. 9. Coupling matrix for (a) pseudo-low-pass and (b) pseudo-high-pass sixpole filter.

Criterion (4) is satisfied by properly choosing each cavity diameter at the middle of the tuning range. Therefore, a uniform plunger displacement incorporating single actuation is adequate to provide an efficient and cost-effective tuning mechanism. The moving part of the tunable filter including tuning plate and six plungers is shown in Fig. 11. Each plunger contains a mode-splitter disc and a sliding contact, as shown in Fig. 11. A conductive elastomer tube is used to provide sliding contact.

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Fig. 12. Tunable filter performance over 500-MHz range. (a) Pseudo-high-pass tunable filter transmission response . Simulation in (red) and measurement (green). (green). (b) Pseudo-high-pass tunable filter return loss

The elastomer has a conductivity of 20 000 S/m, providing adequate conductivity to enclose other modes (particularly TM and TE ). The sliding contact does not affect the TE mode as was described in the previous section. The filter is tuned over the desired tuning range by adjusting the tuning plate attached to the six plungers using a stepper motor. RF tuning performance of both TE tunable pseudo-high-pass and pseudo-low-pass filters are shown in Fig. 12. Fig. 12(a) and (b) includes simulated performance for comparison. The in-band performance is clean and the degenerate TM mode is moved lower as expected. A 500-MHz tuning range is demonstrated through 0.0027-in adjustment of the tuning plate using a stepper motor. Stable tuning performance is achieved. Nominal 3-dB bandwidth at the center of tuning range is 190 and 200 MHz for pseudo-high-pass and pseudo-low-pass filters, respectively. Bandwidth variation is less than 1.5% 3 MHz for both tunable filters over the 500-MHz tuning range. Both filter shapes are stable over the entire 2.5% tuning range. Return loss is maintained at better than 17 and 20 dB for pseudo-high-pass

. Simulation in (red) and measurement

and pseudo-low-pass tunable filters, respectively. To the best of our knowledge, this is the best tuning performance demonstrated in the literature. Near-band rejection performance is stable, particularly for the pseudo-low-pass version where the filter exhibits stable notch levels over the entire measured tuning range. Overall tuning performance for the pseudo-low-pass version is more stable since it uses only long irises for coupling. Measured minimum insertion loss and extracted maintained their value between 0.2–0.22 dB and 15 500–16 000 over the 500-MHz tuning range. The simulated values for insertion loss and are 0.16–0.17 dB and 18 000. Comparing simulated and measured values verifies that the sliding contact is not degrading filter performance. The presented technology has a great advantage over microelectromechanical systems (MEMS) and varactor-based technologies and techniques since it can handle high power and has a potential application for output circuits [22], [23]. Fabricated pseudo-low-pass and pseudo-high-pass tunable filters are used in a cascade configuration, as shown in Figs. 13

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Fig. 12. (Continued.) Tunable filter performance over 500-MHz range. (c) Pseudo-low-pass tunable filter transmission response . tunable filter return loss

. (d) Pseudo-low-pass

Fig. 13. Tunable filter block diagram in a cascade configuration capable of tuning center frequency and bandwidth.

and 14, to realize both bandwidth and center frequency tunability. An isolator is used to connect the two halves of the tunable filter as shown in Fig. 14. Measured tuning performance is shown in Fig. 15. A bandwidth tuning of 40–160 MHz over more than 500-MHz tuning range is exhibited maintaining a very stable in-band and out-of-band performance. The realized tunable filter achieves a step size of 1 MHz. The repeatability of the mechanism was demonstrated over a life test that consisted of 1400 iterations across the 500-MHz tuning range in 125-MHz increments for a total of 11 201 actuations. The total worst case variation of the 3-dB band-edge measured during this test was 0.94 MHz (Fig. 16).

Fig. 14. Cascaded TE tunable pseudo-low-pass and psuedo-high-pass filters to realize full tunable filter with center frequency and bandwidth tenability.

The precision of the fine-tuning performance is shown across the tuning range (single-step) in Fig. 17. A frequency lookuptable (LUT) was constructed from prior measured tuning performance. The measured error with respect to the LUT is shown,

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Fig. 16. Measured

3-dB band edge over 11 201 actuations.

Fig. 17. Measured tuning precision.

Fig. 15. Tunable filter measured performance. Shown is 40–160-MHz bandwidth tuning over more than 500 MHz of center frequency tuning range with a very stable performance. (a) Cascaded filter transmission response. (b) Cascaded filter input return loss. (c) Cascaded filter group delay (normalized, within 3-dB bandwidth). Fig. 18. Measured pseudo-high-pass filter response pre- and post-vibration.

along with the measured 3-dB band edge. The LUT error is within approximately 0.5 MHz. The pseudo-high-pass filter was subjected to random vibration of 12.8 in the planar axes and 21.4 in the out-of-

plane axis. The pre- and post-vibration filter response is shown in Fig. 18. The filter response is unaffected by dynamic loading.

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-BAND FULLY TUNABLE CAVITY FILTER

The details of the mechanism design are beyond the scope of this paper. These data are presented to demonstrate that this filter design can be realized with a robust tuning mechanism capable of achieving excellent tuning resolution and repeatability, while simultaneously withstanding dynamic loads typical of space applications. VI. CONCLUSION A metal-ring loaded TE resonator is shown to offer wide spurious-free window by splitting the degenerate TM mode. The introduced resonator offers tunability without performance degradation. A cross-coupled planar TE cavity resonator incorporating an end-cap metal ring feature and a novel long iris to realize positive coupling in a direct-coupled cavity layout is introduced in this paper. The long iris allows for any transmission zero locations to be realized in a cross-coupled planar TE configuration. Pseudo-low-pass and pseudo-high-pass tunable filters with complex filter function and stable tuning performance were designed and fabricated using the presented idea. Both filters employ the same layout and actuation mechanism. To the best of our knowledge, this is the most stable tunable filter presented in the literature with respect to return loss and transmission zeros. The filter maintains steep selectivity and excellent return loss over the tuning range. A 40–160-MHz bandwidth and 500-MHz center frequency tuning range at the 20-GHz band was exhibited by cascading pseudo-low-pass and pseudo-high-pass tunable filters. The tuning mechanism exhibits a resolution of 1 MHz and a repeatability of 0.94 MHz over an 11 201 actuation life test. The measured tuning error is approximately 0.5 MHz with respect to an LUT. The pseudo-high-pass filter response is maintained after vibration testing. ACKNOWLEDGMENT The authors would like to thank J. Cox, D. Smith, and V. Dokas for performing assembly, tuning, and measurement and S. Choi and K. Engel for providing valuable practical comments and inputs for fabrication.

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[7] R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems. Upper Saddle River, NJ: Wiley, 2007. -band planar TE mode [8] Y. Bahram, Y. Ming, and K. Brian, “A cavity tunable filter using a mode-splitter ring,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 17–22, 2012, pp. 1–3. [9] B. Yassini, M. Yu, and S. Kellett, “A -band high- tunable filter with stable tuning response,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 12, pp. 2948–2957, Dec. 2009. [10] W. Da-Peng, C. Wen-Quan, and P. Russer, “Tunable substrate-integrated waveguide (SIW) dual-mode square cavity filter with metal cylinders,” in Proc. IEEE MTT-S Int. Microw. Workshop Series on Art of Miniaturizing RF and Microwave Passive Components, 2008, pp. 128–131. [11] V. E. Boria, M. Guglielmi, and P. Arcioni, “Computer-aided design of inductively coupled rectangular waveguide filters including tuning elements,” Int. J. RF Microw. Comput.-Aided Eng., vol. 8, no. 3, pp. 226–235, May 1998. [12] T. P. Vuong, G. Fontgalland, R. Crampagne, H. Baudrand, and C. Zanchi, “Tuneable irises for rectangular waveguide filter microwave conference,” in Proc. 30th Eur. Microw. Conf., 2000, pp. 1–4. [13] R. Lech, A. Kusiek, and J. Mazur, “Tuning properties of irregular posts in waveguide junctions—Tunable filter application,” in Proc. 18th Int. Conf. Microw. Radar and Wireless Commun., 2010, pp. 1–4. [14] V. Boria and B. Gimeno, “Waveguide filters for satellites,” IEEE Microw. Mag., vol. 8, no. 10, pp. 60–70, Oct. 2007. [15] E. Pistono, M. Robert, L. Duvillaret, J. Duchamp, A. Vilcot, and P. Ferrari, “Compact fixed and tune-all bandpass filters based on coupled slow-wave resonators,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 2790–2799, Jun. 2006. [16] Y. Liu, A. Borgioli, A. S. Nagra, and R. A. York, “Distributed MEMS transmission lines for tunable filter applications,” Int. J. RF Microw. Comput.-Aided Eng., vol. 11, no. 5, pp. 254–260, Sep. 2001. [17] A. Abbaspour-Tamijani, L. Dussopt, and G. M. Rebeiz, “A millimeterwave tunable filter using MEMS capacitors,” in Proc. 32nd Eur. Microw. Conf., Milan, Italy, Sep. 2002, pp. 813–815. [18] D. Mercier, J.-C. Orlianges, T. Delage, C. Champeaux, A. Catherinot, D. Cros, and P. Blondy, “Millimeter-wave tune-all bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 4, pp. 1175–1181, Apr. 2004. [19] J. Uher and W. J. R. Hoefer, “Tunable microwave and millimeter-wave band-pass filters,” IEEE Trans. Microw. Theory Tech, vol. 39, no. 4, pp. 643–653, Apr. 1991. [20] S. Toyoda, “Variable bandpass filters using varactor diodes,” IEEE Trans. Microw. Theory Tech, vol. MTT-29, no. 4, pp. 363–363, Apr. 1981. [21] A. P. Benguerel and N. S. Nahman, “A varactor tuned UHF coaxial filter,” IEEE Trans. Microw. Theory Tech, vol. MTT-12, no. 4, pp. 468–469, Jul. 1964. [22] S. Lundquist, M. Yu, D. J. Smith, and W. Fitzpatrick, “Application of high power output multiplexers for communication satellites,” in Proc. 20th AIAA Int. Commun. Satellite Syst. Conf. Exhibit, May 12–15, 2002, paper 2002-1992. [23] M. Yu, “Power-handling capability for RF filters,” IEEE Microw. Mag., vol. 8, no. 5, pp. 88–97, Oct. 2007.

REFERENCES [1] W. Graham, T. Glyn, C. Gary, and M. Ian, “Agile equipments for an advanced Ku/Ka satellite,” in Proc. 24th AIAA Int. Commun. Satellite Syst. Conf., San Diego, CA, Jun. 14, 2006, Art. ID AIAA 2006-5396. [2] “Biconical Multimode Resonator,” U.S. Patent 5 614 877. [3] H. L. Thal, Jr, “Cylindrical TE011/TM111 mode control by cavity shaping,” in IEEE Transactions on Microwave Theory and Techniques, New York, Dec. 1979, vol. 27, pp. 982–986. [4] A. E. Atia and A. E. Williams, “General TE011-mode waveguide bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. MTT-24, no. 10, pp. 640–640, Oct. 1976. [5] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-matching Networks, and Coupling Structures. New York: McGraw-Hill, 1964, pp. 921–934. [6] R. J. Cameron, H. G. Grecg, C. J. Radcliffe, and J. D. Rhodes, “Extracted-pole filter manifold multiplexing,” IEEE Trans. Microw. Theory Tech., vol. MTT-30, no. 7, pp. 1041–1050, Jul. 1982.

Bahram Yassini (S’89–M’02) received the M.A.Sc. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 2001. In 2001, he joined COM DEV Ltd., Cambridge, ON, Canada, where he is currently a Principal Member of Technical Staff in the R&D Department. His work includes design, analysis, and modeling of RF/microwave hardware, microelectromechanical systems switches, low-temperature cofired ceramic interconnects, and low-noise amplifiers for ground and space applications. Prior to that, he was with Algorex Canada, where he was involved with RF/wireless channel modeling as an RF Engineer, Italtel SPA, where he was involved with digital radio networks as a Senior Technical Advisor, and MATN, where he was involved with wireless and satellite communication systems as a Senior Radio System Engineer.

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Ming Yu (S’90–M’93–SM’01–F’09) received the Ph.D. degree in electrical engineering from the University of Victoria, Victoria, BC, Canada, in 1995. In 1993, while working on his doctoral dissertation part-time, he joined COM DEV Ltd., Cambridge, ON, Canada, as a Member of Technical Staff. He was involved in designing passive microwave/RF hardware from 300 MHz to 60 GHz for both space- and ground-based applications. He was also a principal developer of a variety of COM DEV’s core design and tuning software for microwave filters and multiplexers, including computer aide tuning software in 1994 and fully automated robotic diplexer tuning system in 1999. His varied experience also includes being the Manager of Filter/Multiplexer Technology (Space Group) and Staff Scientist of Corporate Research and Development (R&D). He is currently the Chief Scientist and Director of the R&D Department, COM DEV Ltd., where he is responsible for overseeing the development of company R&D Roadmap and next-generation products and technologies, including high-frequency and high-power engineering, electromagnetic-based computer-aided design and tuning for complex and large problems, and novel miniaturization techniques for microwave networks. He is also an Adjunct Professor with the University of Waterloo, ON, Canada. He holds NSERC Discovery Grant from 2004 to 2015 with the University of Waterloo. He has authored or coauthored over 100 publications and numerous proprietary reports. He holds eight patents with six more pending. Dr. Yu is an IEEE Distinguished Microwave Lecturer from 2010 to 2012. He has been the IEEE Microwave Theory and Techniques Society (MTT-S) Filter committee Chair (MTT-8) since 2010 and served as Chair of TPC-11. He is an associate editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He was the recipient of the 1995 and 2006 COM DEV Achievement Award for the development a computer-aided tuning algorithms and systems for microwave filters and multiplexers.

Brian F. Keats received the B.A.Sc. degree in mechanical engineering, M.A.Sc. degree in electrical and computer engineering, and Ph.D. degree from the University of Waterloo, Waterloo, ON, Canada, in 2001. 2003, and 2007, respectively. Upon completion of his studies, he joined COM DEV Ltd., Cambridge, ON, Canada, as a Post-Doctoral Fellow, where he has been involved in the design, development, and testing of a variety of products including temperature-compensated filters, tunable filters, and RF switches. He is currently a Senior Member of the Technical Staff with the R&D Department and an Adjunct Lecturer at the University of Waterloo, Waterloo, ON, Canada.

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Multiphysics Modeling of RF and Microwave High-Power Transistors Peter H. Aaen, Senior Member, IEEE, John Wood, Fellow, IEEE, Daren Bridges, Member, IEEE, Lei Zhang, Member, IEEE, Eric Johnson, Member, IEEE, Jaime A. Plá, Member, IEEE, Travis Barbieri, Christopher M. Snowden, Fellow, IEEE, John P. Everett, and Michael J. Kearney

Abstract—In this paper, we present a multiphysics approach for the simulation of high-power RF and microwave transistors, in which electromagnetic, thermal, and nonlinear transistor models are linked together within a harmonic-balance circuit simulator. This approach is used to analyze a laterally diffused metal–oxide–semiconductor (LDMOS) transistor that has a total gate width of 102 mm and operates at 2.14 GHz. The transistor die is placed in a metal-ceramic package, with bond-wire arrays connecting the die to the package leads. The effects of three different gate bond-pad layouts on the transistor efficiency are studied. Through plots of the spatial distributions of the drain efficiency and the time-domain currents and voltages across the die, we reveal for the first time unique interactions between the electromagnetic effects of the layout and the microwave behavior of the large-die LDMOS power field-effect transistor. Index Terms—Electrothermal, global modeling, laterally diffused metal–oxide–semiconductor (LDMOS) transistor, power field-effect transistor (FET).

Fig. 1. Photograph showing the increasing complexity of high-power transistors used in wireless infrastructure products over the past 15 years. The internals of a 45-W 1-GHz and a 60-W 2-GHz transistor (on the left-hand side and center) are compared with a modern 200-W 2-GHz packaged transistor (on the right-hand side). Note the large increase in the number of components and complexity in the matching networks.

I. INTRODUCTION

P

OWER transistors for wireless infrastructure applications have become increasingly complex over the past two decades, from a single die mounted in the package to sophisticated multichip modules, as shown in Fig. 1. Modern high-power devices have total gate widths of several hundred millimeters, achieved by connecting many gate fingers in parallel. The packaged transistors are further complicated by in-package matching networks, comprising several bond-wire arrays connecting metal–oxide semiconductor (MOS) capacitors, and other passive circuit elements, to create the matching Manuscript received July 10, 2012; revised September 24, 2012; accepted September 25, 2012. Date of publication November 29, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. P. H. Aaen, D. Bridges, L. Zhang E. Johnson, J. Plá, and T. Barbieri are with the RF Division, Freescale Semiconductor Inc., Tempe, AZ 85284 USA (e-mail: [email protected]). J. Wood was with Freescale Semiconductor Inc., Tempe, AZ 85284 USA. He is now with Maxim Integrated, San Diego, CA 92121 USA. C. M. Snowden, J. P. Everrett, and M. J. Kearney are with the Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, U.K. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. This paper has supplementary downloadable multimedia material available at http://ieeexplore.ieee.org provided by the authors. This includes video clips, which show visualization of drain current and voltages. This material is 23 MB in size. Digital Object Identifier 10.1109/TMTT.2012.2224366

networks. The 200-W transistor in Fig. 1 contains almost 250 individual bond-wires. Market demands for increased power and efficiency show no sign of abating, and more circuit functions are expected to be integrated within the package. The complexity of the design and construction of high-power microwave transistors continues to increase. In spite of this increasing complexity of the power transistor device, the compact models that are provided by the device manufacturer are often simplified, reducing the arrays of bond wires and capacitors to a few lumped components, and ignoring distributed effects. This has the benefit of reducing the model to only a few essential ports, simplifying the model extraction and speeding up the circuit simulation [1]–[5]. Apart from a few notable exceptions [1], [6]–[13], the internal operation of the packaged transistor is described only coarsely, and the voltages and currents are only available at a few nodes of interest, effectively obscuring the detailed internal operation of the packaged device. Due to this low number of internal nodes, we are limited in our ability to explain poor performance scaling [7], [14], as well as observed temperature distributions that are dependent on frequency, power, and load termination [6]. Fully coupled multiphysics approaches to modeling transistors, where the governing equations are all solved simultaneously, have been developed by a number of researchers [15]–[17]. While undoubtedly valuable for physically small, high-frequency transistors, the physical scale and consequent computational expense prohibit these approaches for

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high-power microwave transistors. To overcome the computational expense, “weakly coupled” approaches have been defined where electromagnetic simulation results (through -parameters), thermal models (through a thermal impedance matrix), and nonlinear electrothermal transistor models are coupled in the netlist of a circuit simulator. This provides a comprehensive description of the transistor for computationally efficient simulation [6]–[8], [12], [18]. Weakly coupled approaches for distributed multiphysics modeling are not without their own expense. For example, schematic representations can become unwieldy, model evaluation can suffer from long simulation time, and data processing can be intense. With the availability of cluster computing, it is possible to simulate circuits containing hundreds of nonlinear transistors, connected to fully distributed matching networks and their interconnections to distributed thermal models. Using this approach, the voltages and currents at all nodes of interest within the packaged device are available, and they can be interrogated to develop a better understanding of its internal operation. In this paper, we present a multiphysics methodology that combines electromagnetic and thermal simulations with nonlinear electrothermal transistor models in harmonic-balance circuit simulations. In Section II, we present the methods by which we develop the constituent models. We also introduce an experiment where the simulation methodology and models are used to explain performance changes exhibited for three different packaged 102-mm LDMOS transistors where modifications have been made to the layout of the gate bond-pad metallization. In Section III, we present a comparison of measured and simulated temperature distributions and large-signal performance. In Sections IV and V, we present for the first time the visualization of the spatially distributed drain efficiency and time-domain voltages and currents across an electrically large die. As will be shown, these visualization methods provide unique insights into the operation of high-power microwave packaged transistors, which can be very beneficial in the development of future designs. Finally, we conclude this paper in Section VI. II. MODEL DEVELOPMENT The packaged LDMOS transistor we examined is illustrated in Fig. 2. This device has 204 individual gates, each having a 500- m unit gate width. The individual transistors are fed in pairs, with two gates attached to the metallization that connects to the gate bond-pad. The individual drains are connected together in a similar way. On the outer edges of the die, only one individual transistor gate is connected to the gate bond-pad. Of the 204 gates, six pairs are not connected to the gate and drain bondpads. These nonfunctioning “dead” fingers were relics of a separate experiment where the output power of the transistor could be tailored with only minor metallization changes. As will be seen, the dead fingers contributed significant detail to the temperature distributions along the center of the die. We used this strategy of defining the power transistor in terms of its constituent electromagnetic, thermal, and nonlinear electronic component parts, to investigate the relationships between the internal behaviors and the terminal performance of the transistor. We have called this strategy a multiphysics modeling

Fig. 2. Illustration of the packaged transistor with a transparent ceramic lid revealing the gate and drain bond-wire arrays and their connection to the LDMOS die. All reference planes of interest are indicated by dashed lines for later reference.

Fig. 3. Illustration of two gate bond-pads with the port connections for the bond-wires and connections to the gates of the transistors. The metallization width, takes on the values 0, 80, and 160 m.

methodology, as it directly couples the important physical environments that affect the operation of the device. We apply the multiphysics modeling methodology to study the effects of changing only the gate bond-pad structure on the device performance. The bond-pad width has values of and m, as illustrated in Fig. 3. For m, the bond-pad has discrete areas for the bond-wires to connect, whereas the m bond-pad is uniformly wide. A packaged device for each value of was measured in a load–pull test bench over a range of input power from 23 to 37 dBm at 2.14 GHz. Harmonic-balance simulations were performed over a range of source and load impedances to simulate load–pull of the packaged transistors. In Sections II-A–II-D, we present the development of each constituent component of the packaged transistor and explain in detail how the multiphysics model is constructed. A. Transistor Model Development Our comprehensive model incorporates a measurement-based nonlinear electrothermal transistor model [19], which was extracted from a 5.0-mm on-wafer transistor. A dense pattern of pulsed I–V and -parameter measurements are taken over the gate–drain voltage space of the transistor, bounded by the maximum drain current, breakdown voltage, and the maximum allowable power dissipation. The manifold structure and the extrinsic network are de-embedded to obtain

AAEN et al.: MULTIPHYSICS MODELING OF RF AND MICROWAVE HIGH-POWER TRANSISTORS

-parameter data at the intrinsic model reference planes [20]. After converting to -parameters, the LDMOS transistor model current and charge state functions ( , , and ) can then be obtained by integration of the small-signal voltage-dependent parameters [14]. This integral formulation for determining the charges ensures a conservative charge formulation, essential for accurate prediction of low-level phase nonlinearity, and for convergence in time-domain simulations [14], [21]. In our model extraction process, we obtain charge data indexed by the intrinsic gate and drain voltages. These data are then approximated using artificial neural networks (ANNs), resulting in smooth and infinitely differentiable 2-D charge functions that are used directly in the model. For the drain current, we use (1) [22, eq. (1)], as this analytical expression has been shown to fit accurately the current data in the near-threshold region. This is typically where the LDMOS power transistor is biased for power amplifier applications (1)

where and are parameters that control the slope in the quadratic region and the transition to the linear region. The parameter allows the slope of the transconductance to be modified in the linear region, is the gate control function, and and are additional fitting parameters. The current in the subthreshold region and between the quadratic region is modeled with , where (2) and is the threshold voltage, controls the abruptness of the “turn-on” characteristic, is the gate-to-source voltage, and is the drain-to-source voltage. The effects of self-heating on the drain current are incorporated using a self-consistent electro-thermal model [23]. A straightforward method of including the thermal effects on the output current is to use a de-rating function on the drain current expression [14], [24], and it can be expressed as (3)

is the drain current measured at where is the temperature, a reference temperature , is the thermal resistance, is the average of the dissipated power (4) is the thermal capacitance. and During a harmonic-balance simulation, the power dissipated as computed by the transistor model is passed to the thermal model. The temperature rise is then computed and it is then passed back to the transistor model. This process continues until convergence is reached. Once the model has been extracted based upon the characterization data obtained from the 5.0-mm transistor, the model is

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Fig. 4. Measured and simulated temperature across a 4.8-mm LDMOS transistor [25].

scaled down to the 500- m unit-gate width. One such model is used to represent each gate finger of the transistor; this is our unitary transistor model. B. Thermal Model Development The thermal model for the entire packaged transistor is obtained through finite-element-based simulations using ANSYS. In these simulations, the bottom of the package flange is held at a constant temperature. All other surfaces are assumed to be adiabatic, and for simplicity, we neglected the heat-spreading effects of the metallization on the die, as well as convective and radiative cooling. As reported in [25], we demonstrate the accuracy of our finiteelement simulations by comparison with measurements of an LDMOS transistor biased under dc conditions to obtain 4.8 W of dissipated power. In this example, the transistor had a total gate width of 4.8 mm, 600- m unit-gate width, 30- m source–drain pitch, is built on an approximately 80- m-thick silicon substrate, and is mounted on top of a 730- m-thick copper carrier. Simulations of the same device were performed and plots of the temperature profiles across the transistor are shown in Fig. 4. The measurements are performed using a QFI InfraScope II system outfitted with a 15 magnification lens resulting in a spot size of 1.6 m. Using the finite-element method, we generate the thermal resistance matrix for the packaged transistor by turning on an incident heat-flux at each finger and then examining the temperature over the whole die, and measuring the temperature at all other fingers. We proceed by exciting each finger in order, until the full thermal resistance matrix is obtained [6]. The temperature for a given finger is defined by averaging the temperature by integration over the finger area. Since the material properties change with temperature, we are careful to perform these single source simulations at temperatures close to those expected in the solution [26]. The thermal resistance matrix for the devices under study has 204 ports, each port being connected to the thermal node of the electro-thermal transistor model, and is written as a Touchstone file for easy inclusion in the circuit simulator.

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Fig. 5. Schematic representation of the connections of the various models within the circuit simulator (from [6]).

C. Electromagnetic Simulations The electromagnetic environment seen by the device plays an important role in its terminal behavior, as will be shown later. This electromagnetic environment includes the on-die metallization of the transistor—the bond pads, the gate and drain metallization structures—and the package and bond-wires that connect the device to the outside world. The metallization structure is simulated using a planar electromagnetic simulator, where the substrate definition has been carefully determined beforehand using transmission line measurements made over the passive and active regions of the transistor [20]. This simulation has ports where the bond-wires connect to the bonding pads and ports where the gates and drains of each unitary transistor connect to the bonding pads. The resulting -parameter model has over 200 ports [13]. The package and bond-wires were simulated using a 3-D finite-element electromagnetic simulation, yielding a multiport -parameter model [27]. This model has two ports representing the connections of the complete device to the external circuit, and ports at the ends of each of the gate and drain bond-wires. These two multiport -parameter models are connected in cascade and enable us to include the model of the electromagnetic environment in a simple manner. D. Model Integration—Enabling Multiphysics Our multiphysics model couples together models of the electromagnetic environment of the transistor, that is the electromagnetic simulations of the package and die metallization, a thermal model of the die, and nonlinear electrothermal models representing each gate finger in the large LDMOS FET die. The constituent component models are generated independently as described in the preceding subsections. Following [6], the gate and drain of each of the 204 unitary transistor models is connected to the appropriate ports of -parameter matrix representing the bond-pad metallizations. The thermal resistance matrix is included through a 204-port (one port for each unitary transistor) impedance matrix. The dissipated power from each unitary transistor model is computed and is provided to the thermal model, which, in turn, provides the temperature increase resulting from the dissipated power and the thermal coupling with the other unitary transistors. Finally, the model for the 102-mm LDMOS die is connected to the ports of the -parameter matrix representing the package and bonding wires. A schematic representation of the connections of the various models is shown in Fig. 5. In a harmonic-balance simulation, each finger is simulated individually, and by monitoring the

Fig. 6. Photograph of the test-fixture used during load–pull measurements of the packaged transistor. Key elements of the fixture are indicated.

voltage and currents at each node in the circuit, we obtain the temperature distribution and we can compute the performance of each unitary transistor. Simulations of the packaged transistor performance for changes in frequency, impedance terminations, or ambient temperatures are readily made. Modifications to the gate bond-pad metallizations are incorporated by changing only the appropriate -parameter file. III. RESULTS A. Measurement Setup The high output power capability of the packaged transistor is achieved by connecting the 204 unitary transistors in parallel. As a result, the input and output impedances that need to be presented to the transistor for optimal operation are very low. Obtaining repeatable load–pull measurements on transistors with very low impedance using mechanical tuners based on 50- slotted transmission lines is very difficult. To overcome the limitations posed by mechanical tuners, pre-matching networks are used to transform the tuner impedances to lower values [28]–[30]. In our test-fixture, a 10:1 transformer, having a 20-dB return loss or better over the frequency range 1.5–3.5 GHz was placed between the tuner and the packaged transistor. The testfixture was characterized using thru-line-reflect (TRL) calibrations for load–pull fixtures [29] and the resulting -parameters were de-embedded from the measurements. A photograph of the test-fixture is shown in Fig. 6, where the microstrip transformers, bias networks, and the 7-mm-to-microstrip connectors are indicated. A thermocouple is mounted through a small hole, approximately 250 m in diameter, directly beneath the package. The thermocouple monitors the temperature at the backside of the package flange during a load–pull measurement. The temperature rise is computed from the difference between the temperature at the top surface, obtained from

AAEN et al.: MULTIPHYSICS MODELING OF RF AND MICROWAVE HIGH-POWER TRANSISTORS

Fig. 7. Comparison of measured versus simulated PAE for the three different gate bond-pad metallizations. The measured results are indicated by dashed lines and solid lines indicate the simulated results.

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Fig. 8. IR images of the die for the bond-pads with m and m. The dashed lines indicate the locations of temperature profiles plotted in Figs. 9 and 10.

infrared (IR) microscopy, and the temperature measured using the thermocouple. B. Two-Port Results The measured and simulated power-added efficiency (PAE) as a function of the input power for the three different gate bond-pad layouts ( m) are shown in Fig. 7. For each measurement and simulation, the load is conjugately matched for maximum efficiency and the source is matched when the transistor is operating at . The uniform bond-pad, m, has approximately 20% higher PAE than the discrete-like bond-pad, m. The overall shapes of the curves and the maximum efficiency values are well predicted, although there is a systematic discrepancy between the measured and simulated data. This difference is indicative of a slightly different source match between the measured and simulated results. Although we have used pre-matching transformers, the mechanical tuners are lossy and have finite steps unlike the continuously variable impedances available during a load–pull simulation. The slightly lower peak efficiencies predicted by the models indicate an increased loss present in the model over that of the measured devices. While not shown here, the agreement between other measured and simulated parameters such as gain and output power are broadly similar. The observed differences do not affect the overall predictive performance of this modeling technique in terms of illustrating the important internal behaviors of the device, as will be demonstrated in Section IV. C. Temperature Distributions While our proposed simulation methodology reports voltages and currents at all of the internal nodes, it is very difficult to verify directly the distributed behavior. Passive and electro-optic field probing methods are an attractive option [31]–[33]. Unfortunately, the construction of the transistor and the closely spaced bond-wires between the gate and the drain prevent standard probes from being lowered close enough to the transistor for sufficient resolution of the fields.

Fig. 9. Measured versus simulated temperature profiles for the packaged tranm. sistor with uniform gate bond-pad

To verify the distributed behavior, we turn to IR microscopy [34] and compare the measured and simulated temperature rise across the center of the die. The packaged transistors were mounted in a test-fixture and excited at approximately 23-dBm input power. The resulting temperature distributions for two of the manifold cases are shown in Fig. 8. The expected broad “upside-down U-shape” temperature distribution is seen for the uniform bond-pad device [25], but for the device with the discrete bond-pads, an interesting triple-peaked distribution is observed. The simulations are able to reproduce the same behavior seen in measurements for both manifolds, as shown in Figs. 9 and 10. The dead finger locations can also be identified as low-temperature regions along the transistor die. The differences between the simulations and measurements are because the IR measurement reports the peak temperature in the middle of each 500- m finger. The simulation uses the thermal resistance matrix that was obtained by averaging the temperature over the unit gate width. The averaging effect of the 1.6- m spot size from the IR camera additionally complicates

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Fig. 10. Measured versus simulated temperature profiles for the packaged tranm. sistor with the discrete gate bond-pad

Fig. 11. Spatially distributed drain efficiency for the device with uniform gate m. bond-pad,

the comparison. It is important to note that the same thermal model is used to compute the temperature rise in Figs. 9 and 10, where only the gate bond-pad layout has been changed. IV. SPATIALLY DISTRIBUTED PERFORMANCE In our simulations, the voltages and currents are available for the dc, fundamental, and all the harmonics specified in the circuit simulation, and at every node of interest in the large circuit. Specifically, during the simulation of these packaged transistors (comprising 204 unitary transistors), we collect voltages and currents from the unitary transistors, the edges of the package, the end of the wires, and both sides of the manifolds, as illustrated in Fig. 2: this amounts to over 1000 nodes. For a harmonic-balance simulation swept over 15 input powers and including three harmonics, this yields a 2-MB text file containing all of the voltages and currents. With this information, we compute the performance of each unitary transistor and plot the data as a function of transistor position along the width of the bond-pad. In Fig. 11, we plot the drain efficiency as a function of the input power and the location of each pair of transistors connected to the drain bond-pad. For the device with the uniform gate bond-pad, m,

Fig. 12. Spatially distributed drain efficiency for the device with discrete gate m. bond-pad,

Fig. 13. Dynamic loadlines for the device with the uniform gate bond-pad plotted as a function of input power, swept from 23 to 34 dBm, in steps of 1 dBm, for the pair of FETs attached to the edge of the drain bond-pad versus a pair of FETs attached half of the distance down the drain bond-pad. Both sets of dym. namic load lines are for the uniform bond-pad,

the efficiency exhibits double peaks with a drop in efficiency at the center of the die. For the device with the discrete bond-pad, m, the drain efficiency surface is remarkably different, with the center of the die exhibiting negative efficiency, as shown in Fig. 12. The center of the die is not generating power as expected, but is, in fact, dissipating power. Using the voltages and currents from the harmonic-balance simulation, we constructed the time-domain waveforms for each pair of unitary transistors that connect to the drain bondpad. Using these waveforms, we plotted the dynamic load lines, over a range of input powers, for a pair of transistors at the end of the drain bond-pad and for another pair in the center, as shown in Fig. 13. Although all unitary transistor models are identical, they are operating dramatically different from one another. This is a consequence of the interactive coupling between the transistor, thermal, and electromagnetic models as described in Section II. In Figs. 14 and 15, we have generated composite plots of the time-domain voltages, currents, and power loss for all

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Fig. 16. Visualization of the drain current as a function of time and location and m (animated version is availwithin the transistor; able by opening the file TMTT-2012-07-0634_Fig16_animation_fullRes.avi). Fig. 14. Time-domain large-signal voltage and current waveforms due to the gate manifold with m.

Fig. 17. Visualization of the drain current as a function of time and location and m (animated version is within the transistor; available by opening the file TMTT-2012-07-0634_Fig17_animation_fullRes. avi).

Fig. 15. Time-domain large-signal voltage and current waveforms due to the m. gate manifold with

unitary transistors. Each plot contains the time-domain waveform for all unitary transistors across the die. By placing each time-domain waveform next to its neighbor, we have in effect created a time-domain surface wave. The wave shows the spatial and temporal distribution of the voltages and currents. By multiplying the voltages and currents at the drains, we can compute the dissipated power per time cycle for each unitary transistor. We demonstrate the effects of changing the gate bond-pad layout by plotting in 3-D the current waveforms for the two limiting cases, and 160 m, as shown in Figs. 16 and 17. We can incorporate the time-dependence and create animations of the output current (or any other time-varying parameter). To the best of the authors’ knowledge, this is the first time that the visualization of the output current as a function of time and position has been created for the entire die.

Fig. 18. Voltages on the gates for each pair of transistors along the two gate bond-pads. Note that in both cases there are significant voltage variations across the transistor. The threshold voltage of the unitary transistor model is indicated (animated version is available by opening the file TMTT-2012-07-0634_Fig18_animation_fullRes.avi).

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Fig. 19. Visualization of the fundamental component of current versus position within the gate bond-pads for the

V. TRANSISTOR PERFORMANCE ANALYSIS The composite plots that show the gate voltage waveforms in Figs. 14 and 15 are surprisingly very different from one another. The maximum gate voltage for the die with m appears at the center of the die much later than it does at the edges. Since this voltage distribution controls the drain current for each individual transistor, the output current from the transistors in the center of the die is also retarded. The maximum gate voltage for the die with m excites practically all unitary transistors simultaneously and the drain current distribution is virtually in-phase across the width of the bond-pad. Note that the vertical lines showing no current are the locations of the nonfunctioning fingers, as described in Section II. From the drain voltage and drain current surfaces, we can compute the dissipated power surface. The plots generated in Figs. 14 and 15, titled “Power Loss,” were computed by taking the product of the instantaneous drain current and drain voltage waveforms. To show only the loss, the values of positive power generation were set to zero, and these are represented by the black regions. The total area of the black region is dictated by the conduction angle of each unitary transistor and the amount of overlap between the current and voltage waveforms. A transistor exhibiting 100% efficiency would be represented by an entirely black plot. Computed powerloss plots for each device show dissipation in the center of the die. This is the reason for the drop in the drain efficiency in the center of the die for the device with the uniform bond-pad and for the huge drop in efficiency for the device with the discrete bond-pad. In fact, for the device with discrete bond-pads, the drain voltage and current surfaces are sufficiently aligned that the center of the transistor is operating as an active resistor. The delayed voltage distribution in the center of the large transistor is a result of the distributed electromagnetic effects from the discrete gate bond-pads in combination with the bond-wires and package, as noted in [7]. In Fig. 18, plots of the voltages applied to gates of the unitary transistors as a function of position along the gate bond-pads are shown. For the device with the discrete bond-pad, the applied

m and

m cases.

gate voltage in the center of the die is much lower than at the ends. This plot shows the voltages at a single instant in time; it represents a single horizontal line on the plots of gate voltage as a function of time and position, as shown in Figs. 14 and 15. If the data traces in Fig. 18 are animated as a function of time, we can show that for the device with the discrete bond-pads, the voltage applied to the unitary transistors in the center of the die is considerably delayed, compared with the voltage applied at the edges. To investigate the origins for the retarded gate voltage due to the discrete bond-pad, we used Sonnet’s commercially available em planar electromagnetic simulator and emvu to plot the current distributions. The large-signal currents on the bond-pads can be generated once the nonlinear circuit simulation is completed. The voltages obtained from the harmonic-balance simulation, at every node connected to the bond-pad, are exported and applied to all of the ports in emvu [35]. The resulting current distribution is the in situ current seen on the manifold while the packaged transistor is in large-signal operation. In Fig. 19, we plot the current for the fundamental frequency, 2.14 GHz for both manifolds, and each plot is on the same current density scale. For the packaged transistor with the discrete bond-pad, large currents flow in the thin metal connecting the discrete bondpads and along the gates of the unitary transistors, as seen in Fig. 19. These transverse currents take time to propagate and the time delay causes the unitary transistors located in the center of the die to conduct later than those at the edges of the die. For the packaged transistor with a uniform gate manifold, minimal transverse currents are observed and there is significantly less voltage variation across the gates of the unitary transistors. VI. CONCLUSION A multiphysics methodology, which combines nonlinear electrothermal transistor models for each individual gate finger with electromagnetic simulations and a thermal model in a nonlinear circuit simulator, has been presented. This methodology was applied to study the effects of different gate bond-pad layouts on the operation of a physically large high-power

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LDMOS transistors. The shape of gate bond-pads was shown to have a large influence on the transistor performance. In the worst case, individual transistors at the center of the die were dissipating rather than generating power. Using distributed multiphysics simulations in this manner, we have produced a “computational microscope” that enables access to all of the voltages and currents throughout the entire structure, revealing behaviors that would have otherwise been hidden using conventional modeling approaches. The insights gained using these techniques will be very useful for future designs. ACKNOWLEDGMENT The authors would like to acknowledge their Freescale Semiconductor Inc., Tempe, AZ, colleagues: C. Dragon for designing the transistors studied in this paper, E. Mares for IR thermal measurements, and J. Crowder for stimulating thermal modeling discussions. The authors would also like to acknowledge the team at Sonnet Software Inc., North Syracuse, NY, for their assistance in the electromagnetic visualization of the manifold currents. REFERENCES [1] M. Rudolph and W. W. Heinrich, “Assessment of power-transistor package models: Distributed versus lumped approach,” in Eur. Microw. Integr. Circuits Conf., Sep. 2010, pp. 86–89. [2] T. Johansson and T. Arnborg, “A novel approach to 3-D modeling of packaged RF power transistors,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 6, pp. 760–768, Jun. 1999. [3] T. Liang, J. Pla, P. H. Aaen, and M. Mahalingam, “Equivalent-circuit modeling and verification of metal-ceramic packages for RF and microwave power transistors,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 6, pp. 709–714, Jun. 1999. [4] P. H. Aaen, J. A. Pla, and C. A. Balanis, “Modeling techniques suitable for CAD-based design of internal matching networks of high-power RF/microwave transistors,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 7, pp. 3052–3059, Jul. 2006. [5] K. Mouthaan, “Modeling of RF high power bipolar transistors,” Ph.D. dissertation, Lab. Electron. Compon., Technol., Mater., Delft Univ. Technol., Delft, Netherlands, 2001. [6] D. Denis, C. M. Snowden, and I. C. Hunter, “Coupled electrothermal, electromagnetic, and physical modeling of microwave power FETs,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 6, pp. 2465–2470, Jun. 2006. [7] K. Goverdhanam, W. Dai, M. Frei, D. Farrell, J. Bude, H. Safar, M. Mastrapasqua, and T. Bambridge, “Distributed effects in high power RF LDMOS transistors,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 333–336. [8] D. Resca, A. Santarelli, A. Raffo, R. Cignani, G. Vannini, F. Filicori, and D.-R. Schreurs, “Scalable nonlinear FET model based on a distributed parasitic network description,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 4, pp. 755–766, Apr. 2008. [9] D. Resca, J. Lonac, R. Cignani, A. Raffo, A. Santarelli, G. Vannini, and F. Filicori, “Accurate EM-based modeling of cascode FETs,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 4, pp. 719–729, Apr. 2010. [10] B. Breitkreutz, F. Schmuckle, and W. Heinrich, “Feeding structures for packaged multifinger power transistors,” in Eur. Microw. Conf., Oct. 2007, pp. 146–149. [11] S. Lee, P. Roblin, and O. Lopez, “Modeling of distributed parasitics in power FETs,” IEEE Trans. Electron Devices, vol. 49, no. 10, pp. 1799–1806, Oct. 2002. [12] M. Rudolph, C. Fager, and D. E. Root, Nonliner Transistor Model Parameter Extraction Techniques. Cambridge, U.K.: Cambridge Univ. Press, 2011, ch. 3, pp. 43–83. [13] P. H. Aaen, J. Wood, D. Bridges, L. Zhang, E. Johnson, T. Barbieri, J. Pla, C. M. Snowden, J. P. Everett, and M. J. Kearney, “Multi-physics modeling of high-power microwave transistors,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3.

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[14] P. H. Aaen, J. A. Plá, and J. Wood, Modeling and Characterization of RF and Microwave Power FETs. Cambridge, U.K.: Cambridge Univ. Press, 2007. [15] R. Grondin, S. El-Ghazaly, and S. Goodnick, “A review of global modeling of charge transport in semiconductors and full-wave electromagnetics,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 6, pp. 817–829, Jun. 1999. [16] A. Cidronali, G. Collodi, G. Vannini, and A. Santarelli, “A new approach to FET model scaling and mmic design based on electromagnetic analysis,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 6, pp. 900–907, Jun. 1999. [17] D. Guerra, D. K. Ferry, M. Saraniti, and S. M. Goodnick, “Millimeterwave power amplifier circuit-device simulations through coupled harmonic balance Monte Carlo particle-based device simulator,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [18] S. Luniya, W. Batty, V. Caccamesi, M. Garcia, C. Christoffersen, S. Melamed, W. R. Davis, and M. Steer, “Compact electrothermal modeling of an -band MMIC,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 651–654. [19] J. Wood, P. H. Aaen, D. Bridges, D. Lamey, M. Guyonnet, D. S. Chan, and N. Monsauret, “A nonlinear electro-thermal scalable model for high-power RF LDMOS transistors,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 2, pp. 282–292, Feb. 2009. [20] J. Wood, D. Lamey, M. Guyonnet, D. Chan, D. Bridges, N. Monsauret, and P. H. Aaen, “An extrinsic component parameter extraction method for high power RF LDMOS transistors,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 607–610. [21] D. E. Root, “Charge modeling and conservation laws,” in Asia–Pacific Microw. Conf. Workshop, Sydney, Australia, Jun. 1999, Session WS2. [22] C. Fager, J. C. Pedro, N. B. de Carvalho, and H. Zirath, “Prediction of IMD in LDMOS transistor amplifiers using a new large-signal model,” IEEE Trans. Microw. Theory Techn., vol. 50, no. 12, pp. 2834–2842, Dec. 2002. [23] D. Bridges, J. Wood, M. Guyonnet, and P. H. Aaen, “A nonlinear electro-thermal model for high power RF LDMOS transistors,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 475–478. [24] P. C. Canfield, S. C. F. Lam, and D. J. Allstot, “Modeling of frequency and temperature effects in GaAs MESFETs,” IEEE J. Solid State Circuits, vol. 25, no. 1, pp. 299–306, Feb. 1990. [25] P. H. Aaen, J. Wood, Q. Li, and E. Mares, “Thermal resistance modeling for the electrothermal layout of high-power RF transistors,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2010, pp. 1672–1675. [26] J. Sofia, “Fundamentals of thermal resistance measurement,” Analy. Techn. Inc., Wakefield, MA, 1995. [Online]. Available: www.analysistech.com/downloads/fundamen.pdf [27] P. H. Aaen, J. A. Pla, and C. A. Balanis, “On the development of CAD techniques suitable for the design of high-power RF transistors,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 10, pp. 3067–3074, Oct. 2005. [28] J. F. Sevic, “A sub 1 ; load–pull quarter-wave pre-matching network based on a two-tier TRL calibration,” in 52nd Fall ARFTG Conf. Dig., Nov. 1998, pp. 73–81. [29] P. H. Aaen, J. A. Pla, D. Bridges, and E. Shumate, “A wideband method for the rigorous low-impedance load–pull measurement of high-power transistors suitable for large-signal model validation,” in 56th Fall ARFTG Conf. Dig., Nov. 2000, pp. 1–7. [30] J. Sirois and B. Noori, “Tuning range analysis of load pull measurement systems and impedance transforming networks,” in 69th Spring ARFTG Conf. Dig., Jun. 2007, pp. 1–5. [31] Y. Gao, A. Lauer, Q. Ren, and I. Wolff, “Calibration of electric coaxial near-field probes and applications,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 11, pp. 1694–1703, Nov. 1998. [32] S. Cripps and A. Porch, “An active, non-intrusive, high resolution microwave field probe with applications in high power RF device and circuit design,” in 2010 IEEE 11th Annu. Wireless Microw. Technol. Conf., Apr. 2010, pp. 1–4. [33] K. Yang, G. David, S. Robertson, J. Whitaker, and L. Katehi, “Electrooptic mapping of near-field distributions in integrated microwave circuits,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 12, pp. 2338–2343, Dec. 1998. [34] M. Mahalingam and E. Mares, “Infrared temperature characterization of high power RF devices,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2001, vol. 3, pp. 2199–2202. [35] P. H. Aaen, L. Zhang, D. Lamey, J. Wood, and S. Arvas, “Visualizing time-domain spatially distributed electromagnetic fields using Sonnet,” in 28th Int. Rev. Progr. Appl. Comput. Electromagn., Columbus, OH, Apr. 2012, pp. 674–679.

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Peter H. Aaen (S’93–M’97–SM’09) received the B.A.Sc. degree in engineering science and M.A.Sc. degree in electrical engineering from the University of Toronto, Toronto, ON, Canada, in 1995 and 1997, respectively, and the Ph.D. degree in electrical engineering from Arizona State University, Tempe, AZ, in 2005. In 1997, he joined the Semiconductor Product Sector, Motorola Inc. (now Freescale Semiconductor Inc.), Tempe, AZ, where he is currently the Manager of the RF Modeling and Measurement Technology Team, RF Division. He has authored over 30 papers and workshop articles in the fields of electromagnetic simulation, package modeling, and microwave device modeling and characterization. He coauthored Modeling and Characterization of RF and Microwave Power FETs (Cambridge Univ. Press, 2007). His current research focuses on the development and validation of multiphysics-based modeling methodologies for high-power and high-frequency electronic devices. Dr. Aaen is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), the IEEE Electron Device Society, and the ARFTG Executive Committee. He is an active member of many technical committees including: MTT-1 Computer-Aided Design and the Technical Program Committee of the IEEE Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS).

John Wood (M’87–SM’03–F’07) received the B.Sc. and Ph.D. degrees in electrical and electronic engineering from The University of Leeds, Leeds, U.K., in 1976 and 1980, respectively. He is currently a Senior Principal Member of the Technical Staff with Maxim Laboratories, Maxim Integrated, San Diego, CA, where he is responsible for system simulation for RF integrated circuits (RFICs). He was a Distinguished Member of Technical Staff responsible for RF computer-aided design (CAD) and modeling with the RF Division, Freescale Semiconductor, Inc, Tempe, AZ. From 1997 to 2005, he was with the Microwave Technology Center, Agilent Technologies (then the Hewlett-Packard Company), Santa Rosa, CA. His areas of expertise include the development of compact device models and nonlinear behavioral models for RF power transistors and ICs. Dr. Wood is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) and the IEEE Electron Devices Society.

Daren Bridges (M’98) received the B.S. degree in electrical engineering from the University of Utah, Salt Lake City, in 1992, and the M.S. degree in electrical engineering from the University of Texas at Dallas, in 1996. In 1992, he joined the RF/Microwave Group, Texas Instruments Incorporated, where he specialized in linear MESFET and HEMT modeling for monolithic microwave integrated circuit (MMIC) devices. In 1997, he joined the Modeling Team, RF Division, Semiconductor Products Sector, Motorola Inc. (now Freescale Semiconductor Inc.), Tempe, AZ. His areas of expertise include RF high-power nonlinear model development and implementation within harmonic-balance simulators and the building and testing of active component model libraries. He has authored or coauthored several papers and workshop articles in the areas of RF and microwave device modeling and simulation.

Lei Zhang (S’03–M’09) received the B.Eng. degree in electrical engineering (with a minor in economics) from Tianjin University, Tianjin, China, in 2000, and the M.A.Sc. and Ph.D. degrees in electrical engineering from Carleton University, Ottawa, ON, Canada, in 2003 and 2008, respectively. She is currently a Modeling Engineer with the RF Modeling Team, RF Division, Freescale Semiconductor Inc., Tempe, AZ. Her expertise includes space mapping, neural networks, automatic model generation of passive and active components, and application of computer-aided design for RF circuits and systems. She has authored or coauthored over 20 technical papers and articles published in journals, conference proceedings, and international workshop notes.

Eric Johnson (M’92) received the B.S. degree in electrical engineering from The University of Michigan at Ann Arbor, in 1989, and the M.S. degree in electrical engineering from the National Technological University, Fort Collins, CO, in 1994. In 1989, he joined Motorola Inc. (now Freescale Semiconductor Inc.), Tempe, AZ, where he was primarily involved in the area of RF and microwave device modeling and characterization for III–V devices. Since 2007, he has been a member of the RF Division, Freescale Semiconductor Inc., where he has been responsible for RF LDMOS device modeling and characterization. He has authored or coauthored a number of papers in the areas of RF and microwave modeling and measurements. His research interests include measurement techniques, measurement automation, and nonlinear device modeling.

Jaime A. Plá (S’87–M’91) was born in Mayagez, PR, in 1969. He received the B.S. degree in electrical engineering from the University of Puerto Rico, Mayagez, in 1991, and the M.S. degree in microwave engineering from the University of Massachusetts at Amherst, in 1993. In 1991, he joined the Microwave Semiconductor Laboratory, Research Division, Raytheon, Lexington, MA, where he was primarily involved with the development of microwave measurement techniques and linear and nonlinear models for monolithic microwave integrated circuit (MMIC) semiconductor devices such as GaAs MESFETs pseudomorphic HEMTs (pHEMTs), and heterojunction bipolar transistors (HBTs). In 1995, he joined the Wireless Infrastructure Systems Division, Semiconductor Product Sector, Motorola Inc. (now Freescale Semiconductor Inc.), Tempe, AZ, where his research is currently centered on the development of high-power RF electrothermal device models for LDMOS devices. His other areas of current interest are the development of package modeling techniques and modeling of passive components, as well as techniques for the measurement of electrical and thermal transistor characteristics related to small- and large-signal modeling extraction and validation.

Travis Barbieri is currently working toward the BSEE degree in electrical engineering at Arizona State University, Tempe. In 2005, he joined Freescale Semiconductor Inc., Tempe, AZ, as an RF Technician. He has provided technical support for several projects dealing with the development and modeling of high-power LDMOS devices. His professional interests include expanding his knowledge of microwave measurements and modeling techniques.

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Christopher M. Snowden (S’82–M’82–SM’91– F’96) received the B.Sc. (Hons.), M.Sc., and Ph.D. degrees from The University of Leeds, Leeds, U.K. Upon graduation in 1977, he was an Applications Engineer with Mullard. His doctoral studies were later conducted in association with Racal-MESL. From 1992 to 2005, he held the Personal Chair of Microwave Engineering with The University of Leeds. From 1995 to 1998, he was the Head of the Department of Electronic and Electrical Engineering, and subsequently Head of the School of Electronic and Electrical Engineering, The University of Leeds. He was the first Director of the Institute of Microwaves and Photonics, School of Electronic and Electrical Engineering, The University of Leeds. From 1989 to 1998, he was a Consultant with M/A-COM Inc. In 1998, he joined Filtronic plc, as the Director of Technology, and in 1999, became a Joint Chief Executive. Until April 2005, he was the Chief Executive of Filtronic ICS, and a Professor of Microwave Engineering with The University of Leeds. He is currently the President and Vice-Chancellor of the University of Surrey, Surrey, U.K. He has authored eight books, over 330 refereed journal and conference papers, and numerous papers. His main research interests include semiconductor device modeling and microwave circuit technology and design. Dr. Snowden is a Fellow of the Royal Society, the Royal Academy of Engineering, and the Institute of Engineering and Technology. He was a Distinguished Lecturer for the IEEE Electron Devices Society until 2005. He was the president of the Institution of Engineering and Technology (2009–2010). He is vice-president of the Royal Academy of Engineering. He was knighted by the Queen during the U.K. New Years Honours in 2012 for services to engineering and higher education. He was the recipient of the 1999 Microwave Prize and the 2009 Distinguished Educator Award of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S). He was the recipient of the 2004 Silver Medal of the Royal Academy of Engineering for his contributions to the compound semiconductor industry. He was also the recipient of the 2012 Outstanding Career Award of the European Microwave Association.

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John P. Everett received the B.Sc. (Hons) degree in physics and astrophysics from Queen Mary and Westeld College, London, U.K., in 1994, and the Ph.D. degree in high-temperature superconductivity and Diploma in experimental solid-state physics from Imperial College, London, U.K., in 1998. Upon graduation, he continued his work with Imperial College, as a Postdoctoral Researcher, where he investigated direct- and alternating-current losses in high-temperature superconducting tapes. In 2006, he joined the Advanced Technology Institute (ATI), University of Surrey, Surrey, U.K., where he has been involved in modeling molecular systems with the support of the Daphne Jackson Trust. Since 2008, he has been with ATI, where he develops nonlinear compact models for RF power laterally diffused metal–oxide–semiconductor devices.

Michael J. Kearney received the B.A. degree in physics from the University of Oxford, Oxford, U.K., in 1985, and the Ph.D. degree from the University of Warwick, Coventry, U.K., in 1988. In 1988, he joined the Long Range Research Laboratory, GEC Hirst Research Centre, London, U.K. After serving a period as Manager of the Long Range Research Laboratory, GEC Hirst Research Centre, in 1995 he joined the Department of Electronic and Electrical Engineering, Loughborough University, as Head from 1997 to 2000. In 2002, he joined Surrey University, as the inaugural Director of the Advanced Technology Institute, and became Head of the School of Electronics and Physical Sciences in 2005. In 2007, he became Dean of the Faculty of Engineering and Physical Sciences, and in 2012, he became a Pro Vice-Chancellor with responsibility for the Research Excellence Framework. He has authored over 100 publications. His research interests include the modeling and simulation of devices for RF and microwave applications, SiGe FETs, and thin-film solar cells.

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Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range Sorin P. Voinigescu, Senior Member, IEEE, Eric Dacquay, Student Member, IEEE, Valerio Adinolfi, Ioannis Sarkas, Student Member, IEEE, Andreea Balteanu, Student Member, IEEE, Alexander Tomkins, Member, IEEE, Didier Celi, and Pascal Chevalier, Member, IEEE

Abstract—This paper describes a methodology for extracting and verifying the high-frequency model parameters of the HICUM L0 and L2 models of a silicon–germanium HBT from device and circuit measurements in the 110–325-GHz range. For the first time, the non-quasi-static effects, missing in the HICUM/L0 model, are found to be essential in accurately capturing the frequency dependence of the transistor maximum available power gain beyond the inflection frequency for unconditional stability. Furthermore, it is demonstrated that the optimal partitioning of the area and periphery components of the junction base–emitter, base–collector, and collector–substrate capacitances, and of the internal and external base and collector resistances can only be determined from -parameter measurements beyond 200 GHz. The extracted models are validated on state-of-the-art linear and nonlinear circuits (amplifier, voltage-controlled oscillator (VCO), and VCO + divider chain) operating at frequencies as high as 240 GHz. Index Terms—Amplifier, -band, device modeling, divider, -band, -band, heterojunction bipolar transistors (HBTs), HICUM, prescaler, silicon-germanium (SiGe), voltage-controlled oscillator (VCO).

I. INTRODUCTION new generation of silicon–germanium (SiGe) heterojunction bipolar transistors (HBTs) with of 300/400 GHz and thick metal back-end makes it possible to design highly integrated low-power transceivers with on-die antennas operating in the 100–300-GHz range [1]. The availability of an HBT compact model, accurate throughout the millimeter-wave range up to 300 GHz, is essential for the development of new millimeter-wave integrated circuit (IC) and system-on-chip (SoC) products. For a variety of reasons,

A

Manuscript received July 11, 2012; revised September 24, 2012; accepted September 25, 2012. Date of publication November 19, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. S. P. Voinigescu, E. Dacquay, V. Adinolfi, I. Sarkas, and A. Balteanu are with the Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada M5S 3G4 (e-mail: sorinv@eecg. toronto.edu). A. Tomkins was with the Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada M5S 3G4. He is now with Peraso Technologies Inc., Toronto, ON, Canada M5J 2L7 (e-mail: [email protected]). D. Celi and P. Chevalier are with STMicroelectronics, F-38926 Crolles, France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2224368

Fig. 1. HBT small-signal equivalent circuit required at the upper millimeterwave frequencies.

until now, the accuracy of HBT compact models has not been verified at frequencies above 170 GHz [2]. The most difficult challenges facing compact modeling of SiGe and InP HBTs in the -band (110–170 GHz), -band (140–220 GHz) and -band (220–325 GHz) are: 1) on-wafer -parameter measurement and de-embedding uncertainty above 110 GHz [2] and 2) the validity of the small-signal equivalent circuit (Fig. 1) at frequencies beyond 110 GHz. From the point of view of small-signal behavior, each diode in Fig. 1 represents a bias-dependent capacitance in parallel with a bias-dependent junction resistance. All three junctions (base–emitter, base–collector, and collector–substrate) are described by area (subscript ) and periphery (subscript ) components. The collector resistance is ) and external ( ) components, and broken into internal ( non-quasi-static (NQS) effects are described by the capacitor , and by the across the internal base resistance transconductance delay . In order to accurately model these devices, de-embedded -parameter data must be acquired and extraction procedures for HBT model parameters must be validated in the same range of very high frequencies. Because inductances of a few picohenrys can have a sizable impact at 200 GHz, the accurate evaluation and de-embedding of the parasitic elements of the wiring stack surrounding the intrinsic device has become very important [2]. One of the most successful compact models for bipolar transistors is the HICUM model. In its most complex Level2 (L2) version, this model addresses high current, NQS, self-heating, and avalanche breakdown, but currently lacks a transconduc. tance delay parameter and the internal collector resistance

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In the last few years, a new HICUM/L0 model has been developed [3]. Compared to L2, the HICUM/L0 version employs a simpler lumped element equivalent circuit, a simplified set of equations, and ignores NQS effects. Although the HICUM/L0 model presents some deficiencies in describing the HBT at very high current injection beyond two times the peakcurrent density, , that region is rarely used in circuit design. As a result, HICUM/L0 is expected to provide adequate accuracy, including self-heating, while requiring a significantly reduced set of model parameters and simulation time. One of the goals of this paper is to confirm or invalidate this expectation. After an experimental investigation of the best calibration and de-embedding methods for on-wafer silicon transistor measurements up to 325 GHz, this paper presents a single-transistor extraction methodology of the HICUM/L0 model for an experimental SiGe HBT process with 280/400 GHz . The accuracy of the L0 model is contrasted with that of the HICUM/L2 version at the transistor and circuit level and is found to be lacking at frequencies beyond 100 GHz. It is believed that this marks the first time that a semiconductor device model was verified at -, -, and -band, demonstrating good agreement between measurements and simulations.

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Fig. 2. Characteristic impedance of a 3.2-mm-long coplanar lines on the commercial alumina ISS: TRL versus LRRM calibration.

II. CALIBRATION AND DE-EMBEDDING UP TO 325 GHz Calibration and de-embedding are critical and necessary steps to achieve precise on-wafer -parameter measurements. If the test structures are carefully designed [2], both LRRM and TRL first-tier calibrations, followed by either transmission-line or OPEN-SHORT de-embedding, have recently been shown to provide “device modeling grade” -parameters for silicon devices from dc to 170 GHz [2]. However, the suitability of these techniques beyond 170 GHz has not yet been established. Figs. 2 and 3 illustrate the measured characteristic impedance and effective permittivity and attenuation, respectively, for a coplanar-waveguide trans3.2-mm long nominally 50mission line fabricated on a commercial alumina impedance standard substrate (ISS) obtained after line-reflect-reflect-match (LRRM) and thru-reflect-line (TRL) calibrations on the same ISS. Remarkably, throughout the -band, the permittivity and attenuation are identical for the two calibration methods. A difference of less than 2% appears between the characteristic impedance values and can be attributed to the fact that, in the TRL calibration, the absolute value of the line impedance is unknown until corrected based on some reference impedance, e.g., the laser-trimmed 50- load on the ISS used in the LRRM calibration. An important observation that can be made from Fig. 3 is that the attenuation of the transmission line on the commercial alumina ISS increases from 2.1 dB/mm at 220 GHz to 5 dB/mm at 325 GHz. These values are comparable to those measured on microstrip lines fabricated in the silicon back-end-of-line (BEOL). They suggest that the use of microstrip matching networks should be avoided in - and -band circuits. Since the -parameters measurements collected with an LRRM calibration require no further correction, the following calibration and de-embedding procedures were applied throughout the rest of the paper.

Fig. 3. Loss and effective permittivity of alumina coplanar lines on ISS: LRRM versus TRL calibration.

First, an LRRM calibration is performed on the commercial ISS. Next, a transmission-line de-embedding step [4], using microstrip lines fabricated on the silicon wafer, is applied to remove the pad and interconnect parasitics up to the device edge in metal 6 (M6 is the uppermost metal in the back-end). This leaves in place all the wiring stack above the device, up to M6. Optionally, a subsequent OPEN-SHORT de-embedding step is finally applied using a local M6-M2 OPEN and a local SHORT from M6 to ground to remove the impact of the wiring stack on top of the HBT between M6 and M2. M1 is not de-embedded. Full-color cross sections of the BEOL and 3-D layout views of the wiring stack on the transistor test structures and of the OPEN and SHORT de-embedding dummy structures can be found in [2]. Although the SiGe HBTs described in this paper are from a faster process run than those in [2], the BEOL, transistor test structure layout, and de-embedding structures are identical. This two-step de-embedding technique allows to accurately predict the performance of the fully wired HBT, as well as to remove the metal stack down to and including M2, as needed for device modeling purposes. The contribution of the M2–M6 metals and vias is thus precisely quantified in an effort to understand the need for L–R–C extraction at the device level in future -, , and -band circuits. An alternate de-embedding approach, where the LRRM calibration on the ISSS is followed by a conventional OPEN-SHORT

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Fig. 4. (a) Measured input/output and ground inductance of the on-wafer global SHORT dummy. (b) Equivalent circuit of the SHORT dummy showing only the inductive parasitics.

de-embedding was also investigated. For the remainder of this paper, we will call this technique: global OPEN-SHORT de-embedding to distinguish it from the t-line de-embedding followed by local OPEN-SHORT de-embedding. The global OPEN and global SHORT both include the pad and the interconnect from the pads to the device down to metal 6 and metal 2, respectively [2]. Fig. 4 reproduces the measured inductive parasitics (from the measured -parameters) of the global SHORT dummy fabricated in the silicon BEOL. The extracted of only 1 pH reground inductance mains practically constant throughout the -band, while the interconnect leading to the device from the input and output pads has inductance values of approximately 20 and 24 pH, respectively. Similarly, Fig. 5 shows the measured capacitances of the global OPEN standard extracted from the mea, sured -parameters where , , and . The impact of 5 pH of base and collector inductances and of a 0.5-pH inductance placed between the emitter and ground on is simulated maximum available power gain (MAG) and in Fig. 6. As can be seen, the inductance of the wiring stack increases and by up to 10% at very high frequencies while MAG remains practically unchanged. The simulations are confirmed by the experimental data in and characteristics are Fig. 7. The measured V, and shown for several bias points of the HBT at varying in 15 mV steps from 750 to 960 mV. The global OPEN-SHORT de-embedding method [2] removes the pads, interconnect between pads, and the device, as well as the inductance associated with the wiring stack above the HBT between

Fig. 5. Measured input/output and coupling capacitance of the on-wafer global OPEN dummy. (b) Equivalent circuit of the OPEN dummy showing only the capacitive parasitics.

Fig. 6. Simulated impact of series base, collector, and emitter inductors de-em. bedding on MAG and

Metal #6 and Metal #2. The Global SHORT standard includes all the vias on the collector and base terminals of the HBT from Metal #6 down to Metal #2, with Metal #2 and Metal #1 shunted together everywhere to form a low-resistance low-inductance ground plane. Transmission-line de-embedding removes the interconnect between the pads and the device only up to the edge of the device and leaves the inductance of the entire wiring stack from Metal #1 to Metal #6 in place above the HBT [2], leading characteristics at frequencies to a flattening out of the beyond 250 GHz [see Fig. 7(a)]. In contrast, the slope of the characteristics does not change with the de-embedding method [see Fig. 7(b)]. Moreover, because it removes the inductance and resistance of the interconnect on top of the deand vice, global OPEN-SHORT de-embedding leads to lower , and [see Fig. 7(c)] than t-line larger de-embedding up to the edge of the device.

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Fig. 8. “Cold” HBT small-signal equivalent circuit showing bias-dependent capacitances and collector–substrate network.

Fig. 9. Extraction of the bias-dependent , , and for a 120 nm 4.5 m CBEBC SiGe HBT from cold HBT -parameters. For 0 V, and V junction bias conditions (measurements: University of Toronto, Toronto, ON, Canada).

Fig. 7. Measured impact of global OPEN-SHORT (dashed red lines in online version) versus t-line de-embedding (solid black lines) to metal 6 on: (a) at -band. (b) , and (c) -band measured , extrapolated at every frequency point. The 120 nm with a 20-dB/decade slope from 4.5 m HBT is biased at V, mV to 960 mV in 15-mV steps.

III. SINGLE-TRANSISTOR HICUM LO EXTRACTION STRATEGY To minimize the interdependency of the extracted parameters, the following step-by-step parameter-extraction sequence was applied: 1) junction capacitances and substrate network; 2) parasitic resistances: , , , ; 3) low and moderate dc current and breakdown parameters; 4) transit time parameters; 5) critical currents; 6) transit time parameters at high injection; 7) thermal resistance; 8) high injection current parameters.

The extraction methodology was first tested on simulated data generated using the HICUM/L0 model. Next the HICUM/L0 parameters of a 120 nm 4.5 m CBEBC SiGe HBT were extracted from dc and -parameter measurements in the 0.1–60and 110–170-GHz frequency range. Later, measurements in the 220–325-GHz range were employed to fine tune the splitting of the base resistance and of the junction capacitances in area and periphery components to better match , , and the -parameters as a function of frequency up to 325 GHz. Version 1.2 of the HICUM/L0 model and HSPICE were used in all simulations. A. Junction Capacitances and Substrate Network These were extracted under “cold” V bias conditions. Consequently, the small-signal equivalent circuit in Fig. 1 reduces to that shown in Fig. 8. The base–emitter and base–collector capacitances were extracted from , , respectively. As can be seen from Fig. 9, either low-frequency or -band data can be used, although shows a slight increase with frequency in the -band. In contrast, because the substrate network consists of the and in parallel, connected in series with the collector–substrate diode, the collector–substrate capacitance, , and the components of the substrate network require both low- and high-frequency measurements. Fig. 10 shows that can be extrapolated from at frequencies below 500 MHz. Once is known, can be obtained from the same plot at high enough frequencies,

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Fig. 10. Extraction of the collector–substrate capacitance and of from low- and high-frequency data for a 120 nm 5 m SiGe HBT (measurements using different test structures: STMicroelectronics, Crolles, France).

Fig. 12. Extrapolation of extraction from under normal forward bias for a 120 nm 4.5 m CBEBC SiGe HBT. conditions and

Fig. 11. Extraction of the substrate resistance from cold HBT -parameter for a 120 nm 5 m SiGe HBT (measurements: STMicroelectronics, Crolles, France).

in the - or -bands, where the substrate network can be approximated by the series combination of and . Similarly, as illustrated in Fig. 11, the substrate resistance can be obtained from at low frequencies when the collector–substrate diode is biased at 0.5 V to minimize the contribution of . B. Parasitic Resistances First, is extracted from the intercept of versus (Fig. 12) under typical forward bias conditions, either from low frequency or from -band data, only at low (0.5 V) to avoid self-heating effects [4]

(1) was also obtained at large forward bias of the base–emitter junction with an open collector from

Fig. 13. Extrapolation of using the Johansen method [5] in the saturation for a 120 nm 4.5 m CBEBC SiGe region at very large currents and HBT.

according to the Johansen method [5]. Again, either low-frequency or -band -parameter data can be employed. The two values are within 18% (Fig. 13). Under the same bias conditions, was extrapolated from at low or high frequencies [5], as shown in Figs. 14 and 15. Finally, Fig. 16 illustrates how the bias-independent part of is determined from at -band under the same open collector bias condition as in the extraction [5]. A somewhat larger and bias-dependent value is obtained from at -band under nominal forward bias conditions. can be estimated from the same set of data at low current densities and low frequency. Aside from this strategy, has been used to implement the so-called circle method (Fig. 17) [6], [7], which, along with fitting , Mason’s , and at - and -bands, has helped in optimizing and to fine tune the optimal splitting between and

VOINIGESCU et al.: CHARACTERIZATION AND MODELING OF SiGe HBT TECHNOLOGY

Fig. 14. Measured versus frequency for extraction from the saturation region for a 120 nm 4.5 m CBEBC SiGe HBT.

Fig. 17. Circle method employed for 4.5 m CBEBC HBT.

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extraction for 120 nm

Fig. 18. Measured versus HICUM/L0 simulated Gummel characteristics for a . 120 nm 4.5 m CBEBC SiGe HBT at Fig. 15. , , and uration region for a 120 nm

extrapolation from -parameter data in the sat4.5 m CBEBC SiGe HBT.

Fig. 19. Measured versus HICUM/L0 simulated output characteristics for a 120 nm 4.5 m CBEBC SiGe HBT.

C. Low and Moderate Current Parameters Fig. 16. ration region in a 120 nm

versus frequency for extraction from satu4.5 m CBEBC SiGe HBT.

, and . This approach is necessary in the absence of tetrode test structures [8], [9], which were not available in this fabrication run.

The model parameters for the collector and base currents at low and medium injection levels, and the avalanche breakdown parameters, were extracted next (Fig. 18). The thermal resistance was obtained from the relative change in in the output characteristics (Fig. 19) as a function of . Note the strong self-heating effect C apparent in the negative slope of the output characteristics making the model parameter extraction particularly challenging.

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Fig. 20. Measured versus HICUM/L0 simulated for a 120 nm 4.5 m CBEBC SiGe HBT biased at V to 1.5 V.

Fig. 21. Impact of NQS on characteristics using HICUM L2 for a 120 nm 4.5 m CBEBC SiGe HBT.

D. Transit Time Parameters Finally, the transit time and transfer current parameters at high injection were extracted from versus and versus measured data and Gummel plot at large injection levels. data conducted throughout the -band were used to extrapolate because the slope of remains approximately constant at 20 dB/decade in this range. As can be seen in Fig. 20, it is relatively easy to obtain excellent agreement between the measured and simulated versus characteristics for values as low as 0.5 V and as high as 1.5 V (close to ). Since the HICUM/L0 model has a simplified lumped equivalent circuit for the base–collector region, and since the exact geometrical dimensions of the internal and external base–collector regions are unknown, the accurate partition of the base–collector capacitance and base resistance was obtained by fine tuning and , while their sum was kept constant, to fit as a function of bias and in the -band, and by fitting , and . and , are particularly important when designing amplifiers, oscillators, and dividers at - and -band. As can be seen from Fig. 21, even when using HICUM/L2, if NQS effects are ignored, the maximum available gain is overestimated immediately above the stability inflection point, and seriously underestimated above 150 GHz. This poses a rather for-

Fig. 22. Measured versus simulated at V, mV to 960 mV in 15-mV steps: (a) using t-line de-embedding up to the edge of the device and (b) using global OPEN-SHORT de-embedding to metal 2.

midable challenge to -, -, and the standard HICUM/L0 model.

-band circuit design using

IV. TRANSISTOR-LEVEL VERIFICATION HICUM/L0 model parameters were extracted for HBTs with 120-nm emitter width and different emitter lengths (2, 3.75, 4.5, and 7.5 m). In this section, a comparison of simulated and measured high-frequency characteristics are illustrated for a 120 nm 4.5 m HBT with one emitter stripe, two base, and two collector contacts. Even when the HICUM/L0 was enhanced with a subcircuit similar to the one in Fig. 1, but without and , it was difficult to compensate for the lack of NQS modeling to simultaneously match , , and from 110 to 325 GHz. However, by moving most of the junction capacitances to the periphery and by optimizing the and splits to compensate for the lack of an internal collector resistance, reasonable agreement could be obtained from dc to 170 GHz. This, however, proved inadequate to model circuits operating at 240 GHz. Instead, the HICUM/L2 model was employed for better device and circuit performance agreement between measurements and simulation. Fig. 22 demonstrates the excellent agreement between the measured and HICUM/L2 simulated characteristics up to the -band, and even up to the -band if global OPEN-SHORT de-embedding is employed to remove the inductance of the

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A. 240-GHz Amplifier

Fig. 23. Measured versus simulated at V, mV to 960 mV in 15-mV steps: (a) using t-line de-embedding up to the edge of the device and (b) using global OPEN-SHORT de-embedding to metal 2.

A three-stage cascode amplifier, whose schematic is shown in Fig. 25, was designed using a preliminary model based on device simulation. To ensure the stability of the cascode stages in the presence of the unavoidable inductance associated with the bias-decoupling capacitor, feedback resistors were connected between the base and the collector of the common base HBTs [11]. All stages are biased at the peak current density of 14 mA/ m for a total power consumption of 34 mW from a 2.5-V supply. The die photograph of the amplifier is reproduced in Fig. 26. The input, output, and interstage matching networks were implemented with coupled line impedance transformers [12] since the simple shunt L- series C matching networks in this frequency range would require very small capacitors. The coupled microstrip lines were formed in the top, 3- m-thick copper layer with the bottom three metals shunted together to form the ground plane. The measured loss of a 50- microstrip line, with identical cross section and ground plane to the one used in the coupled lines, varies between 2.5–3 dB/mm from 220 to 270 GHz. A large proportion of the power gain of the cascode is therefore lost on the coupled transmission-line network. In retrospect, as in SiGe HBT -band amplifiers [13] and in recent 300-GHz SiGe HBT signal sources [14] fabricated in the same back-end, matching networks with transformers and inductors may prove less lossy than coupled line matching networks. This aspect needs to be systematically investigated. Fig. 27 compares the measured with the simulated -parameters using the HICUML2 model and the HICUML0 model, which does not capture NQS effects. The inductance of the decoupling capacitor, in the 1–2-pH range, was found to have a significant impact on the simulated power gain. All passive elements, including larger areas of the amplifier layout, were simulated as multiports using the commercial electromagnetic (EM)-field simulator EMX.1 These results demonstrate the importance of the NQS effects in predicting the gain of the amplifier at frequencies approaching the and of the transistor. B. 150-GHz VCO and Prescaler

Fig. 24. Measured versus simulated to 960 mV in 15-mV steps.

at

V,

mV

wiring stack above the device. Similar agreement can be observed for in Fig. 23 and characteristics in Fig. 24. V. VALIDATION ON

- AND

-BAND CIRCUITS

The single-transistor models, validated on small-signal transistor -parameter measurements up to 325 GHz, were next used to fine-tune geometry-scalable HICUM/L2 and HICUM/L0 models. The latter were employed to confirm the measured performance of linear and nonlinear circuits in the 140–240-GHz range. It is important to note that these benchmark circuits employ different transistor sizes than those measured for parameter extraction.

A breakout consisting of a fundamental Colpitts–Clapp VCO and a divide-by-16 prescaler was fabricated as the most critical blocks required in the phase-locked loop (PLL) of future fundamental 150- or 300-GHz harmonic transceivers. Their schematics are shown in Fig. 28 and are similar to those fabricated in an older production technology [1]. The only difference are the varactors in the VCO, which are realized from SiGe HBTs with short-circuited base–emitter junctions. At the input of the prescaler is a dynamic divider followed by three static divider stages, all operating from a nominal supply voltage of 1.5 V. The VCO-prescaler operates from 138 to 148 GHz, limited by the tuning range of the VCO. Its phase noise was measured throughout the band, at the divider output, and was found to vary from 80 to 81 dBc/Hz, at 1-MHz offset when accounting for the divider ratio (24 dB). The output 1Integrand Softw. Inc., Berkeley Heights, NJ. [Online]. Available: http://www.integrandsoftware.com/

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Fig. 25. Amplifier schematic.

Fig. 26. Die photograph of the 240-GHz amplifier.

Fig. 27. Comparison of measured and simulated amplifier -parameters.

power of the standalone VCO breakout varies from 5 to 11 dBm in the 138–148-GHz tuning range. The prescaler was verified to divide correctly by 16 when the supply voltage was varied between 1.4–1.8 V. Similarly, the VCO oscillates for values ranging from 1 to 2 V. The VCO core consumes 35 mW from 1.5 V, and the divider chain, without output buffers, draws 42.5 mA from 1.5 V. The VCO, prescaler, and buffers consume a total of 120 mW from a 1.5-V supply.

Fig. 28. VCO and prescaler schematics.

Fig. 29. Measured versus simulated VCO tuning range.

Fig. 29 illustrates the measured and HICUM/L2 simulated tuning characteristics of the standalone VCO at two supply voltages of 1.5 and 2 V, respectively. The agreement is better than 8%. However, for varactor control voltages larger than 3 V, the avalanche breakdown model causes convergence problems. The match between measurements and simulations could be further improved by optimizing the area and periphery junction capacitance parameters and . Note that the measured tuning

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characteristics are insensitive to the supply voltage, whereas the simulation results show some VCO pulling. Finally, it should be noted that the simulations predicted a decrease of about 2 GHz in the VCO tuning frequency when the VCO was loaded by the divider chain. A larger decrease of about 4 GHz was observed in measurements. Despite these promising results, unsolved problems remain regarding the accuracy of t-line and global OPEN-SHORT de-embedding in the -band, and the ability of the HICUM model, both L0 and L2, in predicting the correct frequency dependence of in the 5–50-GHz range. VI. CONCLUSION The HICUM L0 and L2 models were extracted for the first time from -, -, and -band -parameter measurements for a 400-GHz SiGe HBT process. Good agreement between the measured and simulated transistor - and -parameters, , and , in the dc to 170-GHz range was demonstrated for the L0 model. However, when tested on circuits, the L0 model was found to underestimate the gain of a three-stage 240-GHz amplifier and the negative resistance of a 150-GHz VCO. It was only when measurements in the 220–325-GHz range were performed that the limitations of the L0 model in correctly predicting the NQS effects and the characteristics became apparent. In contrast, the HICUM/L2 model, including NQS effects and a more sophisticated distributed small-signal equivalent circuit appears to be adequate for circuit simulation up to 325 GHz. Its accuracy was validated on a 240-GHz threestage cascode amplifier and on a low-power fundamental-frequency 120-mW 150-GHz VCO prescaler. ACKNOWLEDGMENT The authors would like to acknowledge STMicroelectronics, Crolles, France, for donating the chips, compuer-aided design (CAD) tools from the Canadian Microelectronics Corporation (CMC) and equipment grants from the Natural Sciences and Engineering Research Council of Canada (NSERC), and CFI. Many thanks are also due to J. Pristupa, for his always prompt and outstanding CAD support. REFERENCES [1] I. Sarkas, J. Hasch, A. Balteanu, and S. P. Voinigescu, “A fundamental frequency 120-GHz SiGe BiCMOS distance sensor with integrated antenna,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 3, pp. 795–812, Mar. 2012. [2] K. H. K. Yau, E. Dacquay, I. Sarkas, and S. P. Voinigescu, “On-wafer silicon device and circuit characterization above 100 GHz,” IEEE Microw. Mag., vol. 13, pp. 30–54, Feb. 2012. [3] M. Schröter, S. Lehmann, S. Fregonese, and T. Zimmer, “A computationally efficient physics-based compact bipolar transistor model for circuit design—Part I: Model formulation,” IEEE Trans. Electron Devices, vol. 53, no. 2, pp. 279–286, Feb. 2006. [4] A. M. Mangan, S. P. Voinigescu, M. T. Yang, and M. Tazlauanu, “Deembedding transmission line measurements for accurate modeling of IC designs,” IEEE Trans. Electron Devices, vol. 53, no. 2, pp. 235–241, Feb. 2006. [5] S. P. Voinigescu, M. C. Maliepaard, J. L. Showell, G. Babcock, D. Marchesan, M. Schröter, P. Schvan, and D. L. Harame, “A scalable high frequency noise model for bipolar transistors with application to optimal transistor sizing for low-noise amplifier design,” IEEE J. SolidState Circuits, vol. 32, no. 9, pp. 1430–1438, Sep. 1997.

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[6] T. Johansen, V. Krozer, D. Hadziabdic, C. Jiang, A. Konczykowska, and J.-Y. Dupuyt, “” A novel method for HBT intrinsic collector resistance extrcation from -parameters,” in Proc. Asia–Pacific Microw. Conf., 2007, pp. 1–4. [7] T. Nakadai and K. Hashimoto, “Measuring the base resistance of bipolar transistors,” in IEEE Bipolar Circuits Technol. Meeting, 1991, pp. 200–2003. [8] W. J. Kloosterman, J. C. J. Paasschens, and D. B. M. Klaassen, “Improved extraction of base and emitter resistance from small signal high frequency admittance measurements,” in IEEE BCTM, 1999, pp. 93–96. [9] H.-M. Rein and M. Schröter, “Experimental determination of the internal base sheet resistance of bipolar transistors under forward-bias conditions,” Solid State Electron., vol. 34, no. 3, pp. 301–308, 1991. [10] M. Schröter and S. Lehmann, “The rectangular bipolar transistor tetrode structure and its application,” in IEEE Int. Microelectron. Test Structures Conf., Tokyo, Japan, Mar. 19–22, 2007, pp. 206–209. [11] K. W. Kobayashi, R. Esfandiari, and A. K. Oki, “A novel HBT distributed amplifier design topology based on attenuationcompensation techniques,” IEEE Trans. Microw. Theory Techn., vol. 42, no. 12, pp. 2583–2589, Dec. 1994. [12] T. Jensen, V. Zhurbenko, V. Krozer, and P. Meincke, “Coupled transmission lines as impedance transformer,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 12, pp. 2957–2965, Dec. 2007. [13] E. Dacquay, A. Tomkins, K. H. K. Yau, E. Laskin, P. Chevalier, A. Chantre, B. Sautreuil, and S. P. Voinigescu, “ -band total power radiometer performance optimization in an SiGe HBT technology,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 3, pp. 813–826, Mar. 2012. [14] A. Tomkins, E. Dacquay, P. Chevalier, J. Hasch, A. Chantre, B. Sautreuil, and S. P. Voinigescu, “A study of SiGe signal sources in the 220–330 GHz range,” presented at the IEEE BCTM, Portland, OR, Oct. 2012.

Sorin P. Voinigescu (S’91–M’95–SM’02) received the M.Sc. degree in electronics from the Polytechnic Institute of Bucharest, Bucharest, Romania, in 1984, and the Ph.D. degree in electrical and computer engineering from the University of Toronto, Toronto, ON, Canada, in 1994. From 1994 to 2002, he was initially with Nortel Networks, Ottawa, ON, Canada, and then with Quake Technologies, Ottawa, ON, Canada, where he was responsible for projects in high-frequency characterization and statistical scalable compact model development for Si, SiGe, and III–V devices. He later conducted research on wireless and optical fiber building blocks and transceivers in these technologies. In 2002, he joined the University of Toronto, where he is a currently a Full Professor. His research and teaching interests focus on nanoscale semiconductor devices and their application in ICs at frequencies beyond 300 GHz. From 2008 to 2009, he spent a sabbatical year with Fujitsu Laboratories of America, Sunnyvale, CA. Dr. Voinigescu is a member of the ITRS RF/AMS Committee and of the TPCs of the IEEE CSICS and BCTM. He was the recipeint of the 1996 Nortel President Award for Innovation. He was a corecipient of the Best Paper Award of the 2001 IEEE CICC and the 2005 IEEE CSICS. He was also a corecipient of the Beatrice Winner Award of the 2008 IEEE ISSCC. His students have been recipients of the Student Paper Award of the 2004 VLSI Circuits Symposium, the 2006 SiRF Meeting, RFIC Symposium and BCTM, and the 2008 and 2012 IEEE Microwave Theory and Techniques (IEEE MTT-S) International Microwave Symposium (IMS).

Eric Dacquay (S’04) received the B.A.Sc. degree in computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2008, and is currently working toward the M.A.Sc. degree in electrical engineering at the University of Toronto, Toronto, ON, Canada. His current research interests are in the areas of passive millimeter-wave imaging and detector modeling for silicon wafer scale imaging arrays

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Valerio Adinolfi received the Laurea degree and Laurea Magistrale Master degree in electrical engineering from the Universita‘ degli studi Roma Tre, Rome, Italy, in 2009 and 2011, respectively, and is currently working toward the Ph.D. degree in electrical engineering at the University of Toronto, Toronto, ON, Canada. His research interests are in quantum dot electronic devices.

Ioann Sarkas (S’04) received the Diploma degree in electrical engineering from the University of Patras, Patras, Greece, in 2006, the M.A.Sc. degree in electrical and computer engineering from the University of Toronto, Toronto, ON, Canada, in 2010, and is currently working toward the Ph.D. degree in electrical and computer engineering at the University of Toronto.

Andreea Balteanu (S’10) received the B.A.Sc. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 2007, the M.A.Sc. degree from the University of Toronto, Toronto, ON, Canada, in 2010, and is currently working toward the Ph.D. degree at the University of Toronto. She has previously held internships with the IBM T. J. Watson Research Center, the Altera Corporation, and Texas Instruments Incorporated. Her research interests include the design of high-speed and millimeter-wave ICs. Ms. Balteanu was the recipient of the Best Student Paper Award of the 2012 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS).

Alexander Tomkins (M’12) received the B.A.Sc. degree in engineering physics from Carleton University, Ottawa, ON, Canada, in 2006, and the M.A.Sc. degree from the University of Toronto, Toronto, ON, Canada, in 2010. Since 2011, he has been with Peraso Technologies Inc., Toronto, ON, Canada, where he designs millimeter-wave transceivers for low-power and mobile applications.

Didier Céli received the Electrical Engineering degree from the Ecole Supérieure d’Electricité, Gif-surYvette, France, in 1981. In 1982, he was with the Semiconductor Division, Thomson-CSF. He is currently with Central Research and Development, STMicroelectronics, Crolles France, where he has been involved in the field of modeling for advanced bipolar and BiCMOS technologies, including model development, parameter measurement, and extraction tools. He is currently responsible for the BiCMOS Device Modeling Group, as a Technical Expert. He also gives lectures and training courses on compact device modeling in engineering schools. He has authored or coauthored several technical papers related to his research. Mr. Céli was a member of the CAD/Modeling Subcommittee of IEEE Bipolar/BiCMOS and Technology Meeting (1998–2004).

Pascal Chevalier (M’06) was born in Saumur, France, in 1971. He received the Engineering degree in science of materials from the University School of Engineers of Lille, Lille, France, in 1994, and the Ph.D. degree in electronics from the University of Lille, Lille, France, in 1998. His doctoral research concerned the development of 0.1- m InP-based HEMT technologies. In 1999, he joined Alcatel Microelectronics, Oudenaarde, Belgium, where he contributed to the start of RF BiCMOS and led the development of 0.35- m SiGe BiCMOS technologies. In 2002, he joined STMicroelectronics, Crolles, France, where he has been involved in the development of 0.13- m SiGe BiCMOS technologies and led the research on advanced RF and millimeter-wave silicon-based devices such as SiGe HBTs and Si LDMOS transistors for CMOS derivatives technologies. He currently manages BiCMOS process integration research and development and is a Senior Member of Technical Staff. He has authored or coauthored approximately 120 technical journal papers and conference publications. Dr Chevalier has been the chair of the Process Technology Subcommittee for the IEEE Bipolar/BiCMOS Circuits and Technology Meeting. He belongs to the RF and AMS Technologies Working Group, ITRS, which he leads the Silicon Bipolar and BiCMOS Subgroup.

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Resistive Graphene FET Subharmonic Mixers: Noise and Linearity Assessment Michael A. Andersson, Student Member, IEEE, Omid Habibpour, Student Member, IEEE, Josip Vukusic, Member, IEEE, and Jan Stake, Senior Member, IEEE

Abstract—We report on the first complete RF characterization of graphene field-effect transistor subharmonic resistive mixers in the – GHz. The analysis includes confrequency interval version loss (CL), noise figure (NF), and intermodulation distortion. Due to an 8-nm thin Al O gate dielectric, the devices operate at only 0 dBm of local oscillator (LO) power with an optimum measured CL in the range of 20–22 dB. The NF closely mimics the CL, thus determining the noise to be essentially thermal in origin, which is promising for cryogenic applications. The highest input third-order intercept point is measured to be 4.9 dBm at an LO power of 2 dBm. Index Terms—Field-effect transistors (FETs), graphene, intermodulation distortion (IMD), noise measurements, subharmonic resistive mixers.

G

I. INTRODUCTION

RAPHENE HAS recently attracted great attention in the field of nanotechnology aimed at RF and microwave electronics [1], [2]. This was made possible by the first isolation of graphene, a one-atom layer sheet of carbon atoms organized in a honeycomb lattice, together with the demonstration of the field effect, in 2004 [3]. Since then, the graphene synthesis methods have advanced, making it a promising candidate comparing it to, for example, carbon nanotubes (CNTs). The potential for field-effect transistors (FETs), derived from the graphenes high intrinsic carrier mobility for both electrons and holes, 100 000 cm V s, and the high carrier saturation velocities of 4 5 10 cm s has been thoroughly investigated, as recently reviewed in [4]. Ultimately, graphene field-effect transistors (G-FETs) with and in excess of 1 THz are projected, in the limit of channel length down-scaling and eliminating the currently deteriorating device parasitics [2]. Moreover, graphene has the unique property to switch between the n- and p-channel by electrical gating and distinctive properties useful in, e.g., opto-electronics [5] and sensor applications [6]. Since the realization of the first top-gated G-FET in 2007 [7], there have been considerable efforts to go to higher frequencies. The high-frequency capabilities demonstrated are far from Manuscript received July 10, 2012; revised September 17, 2012; accepted September 20, 2012. Date of publication October 18, 2012; date of current version December 13, 2012. This work was supported in part by the Swedish Foundation of Strategic Research (SSF) and in part by the Wallenberg Foundation (KAW). This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with the Terahertz and Millimetre Wave Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-412 96 Göteborg, Sweden (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2221141

the intrinsic potential with published GHz [8]. Suitability of G-FETs for microwave circuit applications has been investigated, resulting in high spectral purity frequency multipliers [9] and fundamental transconductance mixers [10], [11] with a best conversion loss (CL) of 27 dB at 4 GHz, a subharmonic resistive mixer with a CL of 24 dB [12] at 2 GHz, and a 10-dB small-signal power amplifier operating at 1 GHz [13]. In addition, an RF rectifying detector, with a linear and high dynamic range response up to 50 GHz [14], has been presented. While GaAs FET active mixers can provide 6–10-dB conversion gain [15], resistive G-FET mixers are behind mature GaAs HEMT counterparts, where fundamental [16] and subharmonic [18] designs achieve CL of 5.3 and 6.5 dB, respectively. Further performance analysis beyond measuring the CL, in terms of noise and intermodulation performance, is still sparse for G-FET mixers, with a single value for an input third-order intercept point (IIP3) of 13.8 dBm reported at 10 MHz for a fundamental transconductance mixer [10]. In this paper, we expand the characterization for the G-FET resistive subharmonic mixer of [19], which included the CL and noise figure (NF). This represented the first study of noise at microwave frequencies for a G-FET, while previous studies considered only low-frequency noise and phase noise [20]. The addition includes intermodulation distortion (IMD) of the mixer as examined via two-tone measurements to extract the IIP3, which, besides the CL and NF, represents the most important quantity to study for a microwave mixer from a systems perspective. Finally, the large-signal model of [21] is utilized to validate the IMD results.

II. MOTIVATION FOR RESISTIVE G-FET MIXERS There are basically two operating principles for an FET mixer: either utilizing the change in transconductance or channel conductance (resistance) with gate–source voltage. In both approaches, a local oscillator (LO) signal is applied to the gate to achieve a resulting time-varying periodic quantity or . The former case is referred to as an active transconductance mixer, where the RF signal is applied to the gate, and the latter to a resistive mixer, with the RF signal applied to the drain. The LO pumped time-varying quantity, either or , may be expressed as a Fourier cosine series in terms of LO frequency harmonics [22]

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where the first-order coefficient of is responsible for the efficiency of fundamental mixing and the second-order coefficient is responsible for subharmonic mixing. The best possible performance from a transconductance mixer is realized by maximizing the variation in , which is accomplished by biasing the FET in current saturation [15]. Under these conditions, the active FET mixer can provide a maximum conversion gain expressed with its small-signal circuit elements and the coefficient as [22] (2) Contrary to active mixers, for a resistive mixer the drain is unbiased. It is limited to a CL, which was analyzed in [16], with the aim of acquiring an intuitive expressions in terms of device parameters, for an understanding of the mixer operation and preliminary design work. The analysis is done in terms of the reflection coefficient, as seen from the drain port . This assumes that all mixing terms are terminated in a matched load, the real system impedance . The best performance assumes to be a 0.5 duty-cycle square wave and yields

Fig. 1. Optical image of fabricated device with two gate fingers, yielding m. Scale bar is 10 m.

. which is consistent with the fact that As a consequence of the currently low transconductance in G-FETs and the lack of clear current saturation, the thus far reported G-FET transconductance mixers have shown poor performance with a high CL. Instead, presently it is more promising to use the resistive mixing concept. Importantly, it currently also makes the best utilization of the unique transport properties of graphene for a novel concept to do subharmonic mixing with a single FET. The extension to a subharmonic resistive design in conventional FETs is done, for example, by a parallel configuration where the LO is applied 180 out-of-phase to the gates of two devices [18]. Since this requires a balun, the G-FET subharmonic mixer allows a more compact circuit.

our G-FET resistive mixer, the device dimensions are chosen to be m and m based upon the reasoning in [12]. The actual devices were fabricated on graphene flakes produced by mechanical exfoliation on 300-nm silicon dioxide. The drain and source pads were formed via an electron beam lithography exposure and subsequent evaporation of 1-nm Ti, 15-nm Pd, and 60-nm Au, and liftoff. The thin layer of Ti is used for improved adhesion, while the Pd layer is known to simultaneously provide good contact resistivity and symmetric transfer characteristics. A stepwise natural oxidation, while heated on a hotplate, of electron beam evaporated Al was used to grow an 8-nm-thick Al O gate oxide. The aim was to reduce the LO power requirement compared to previous work since the higher gate capacitance per area reduces the required gate swing voltage. A second electron beam lithography step was used to define a top-gate electrode, which uses a similar metallization stack with more Ti consisting of 4-nm Ti, 15-nm Pd, and 60-nm Au. The above-described methods were used to fabricate three devices with slightly different performance, as will be subsequently indicated. Device #1 was used for original NF characterization first presented in [19] and device #2 was produced for the intermodulation analysis of this extended paper. Since device #2 had a too high leakage current, the gate voltage analysis was performed with device #3, with the main purpose of comparison to model simulations. A magnified optical photo of a two-finger G-FET device characterized in this paper is shown in Fig. 1.

III. DEVICE DESIGN AND FABRICATION

IV. RF MEASUREMENT SETUPS

The device design was focused on minimizing the mixer CL. Since [11] for resistive mixers, the above discussion translates this into a high on–off ratio, i.e., and . This is also true for the timevarying wave shape resulting from the symmetric transfer characteristics of a G-FET. In order to optimize the conditions for

The mixer operation is based on a sinusoidal LO signal applied to the gate of the G-FET, biased at the point of minimum conductivity (Dirac voltage). Due to the electron–hole duality of the graphene channel conduction, the on and off states are swept twice in one LO cycle and the resistance variation, as seen from the drain, , has a fundamental frequency component

(3) and , correFurther, the ideal case with sponding to resistance states and , results in a minimum CL of 3.9 dB. This is to be compared to a CL of 3 dB for an ideal double-sideband (DSB) mixer with all terms, except the image ideally terminated and a CL of 0 dB if the image is also reactively terminated [17]. Since the mixing is related to the coefficient of (1), in addition to the on-off ratio, the CL decreases with an alteration of the wave shape. Making the time-varying shape triangular instead yields (4)

ANDERSSON et al.: RESISTIVE G-FET SUBHARMONIC MIXERS

Fig. 2. Setup for measuring the G-FET subharmonic mixer NF in a 50system. Details are in Section IV-A.

at twice . Thus, the multiplication with , applied to the drain terminal, contains terms of the form , including the desired IF component for subharmonic down-conversion [12] with the frequency spacing utilized to separate the RF and IF signals at the drain. All RF measurements were performed on chip using a probe station. A. NF Measurement Setup The complete measurement setup for the mixer noise is shown in Fig. 2, the core being the Agilent N8975A noise figure analyzer (NFA). It was used to determine both the CL and NF versus frequency in the range – GHz with the measurement frequency set to MHz. The system was calibrated to account for the noise generated by the NFA itself and also the known losses in the setup on the signal path from the noise source to the NFA. A broadband noise source, with dB dB in the relevant frequency range, was utilized to increase the -factor, and thus the measurement accuracy. The signal separation at the drain terminal was performed with a directional coupler having 10-dB coupling in the frequency range of 1–18 GHz. The RF noise signal is coupled to the drain of the G-FET and the reflected signal at MHz is transmitted directly to the NFA since it is out of the coupler bandwidth. Similarly, noise in the measurement bandwidth originating from the matching termination connected at port 2 is not coupled to the NFA. An additional 40-dB isolation between port 1 and port 4 at the measurement frequency of 100 MHz is provided by an external SMA high-pass filter to assure that the measured noise originates from the mixer and not the noise source. The filter characteristic is flat up to 5 GHz, which sets the upper limit on the measurement frequency. B. IIP3 Measurement Setup The well-established two-tone measurement principle [15] is used for the IMD measurement, as presented in Fig. 3. The setup thus uses in total three signal generators. The two equal-power RF signals are chosen to be at closely spaced frequencies and separated by 20 MHz, e.g., GHz and GHz. With a standard power combiner at port 1 of the directional coupler, the two RF signals are coupled to the drain of the G-FET, connected at port 3. The directional coupler has

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Fig. 3. Two-tone measurement setup for examination of the G-FET subharmonic mixer IMD (IIP3) in a 50- system. The details are outlined in Section IV-B.

a 3-dB coupling factor to allow for high enough input powers to the mixer needed to detect the weak third-order response. The resulting lower frequency signals are transmitted directly from port 3 to port 4 of the coupler and monitored with a spectrum analyzer. The expected down-converted linear responses while pumping with frequency GHz are at the frequencies MHz and MHz and the corresponding third-order IMD responses are consequently at MHz and MHz. The same intermediate and third-order intermodulation frequencies were used to measure in the interval – GHz. Port 2 of the directional coupler is again terminated in a matched load, . First, a verification of the integrity of the measurement setup was done, to ascertain that the signals at 130 and 70 MHz originate from the device and not from mixing of the outputs between different harmonics of the signal generators. Connecting the spectrum analyzer directly to the output of the power combiner, only the two fundamental tones were observed for the relevant input signal levels. V. MEASUREMENT RESULTS AND DISCUSSION To evaluate the mixing capabilities of the fabricated devices, a dc characterization is made. The main purpose is to find the drain-to-source resistance, as presented in Fig. 4, for both devices together with the model fitted curves [21]. The devices exhibit different on–off ratios , and , respectively, with the other parameters summarized in Table I. Mainly the contact resistances and mobilities differ, while device #2 exhibits a slightly larger asymmetry with . A gate–oxide capacitance of 0.5 F cm is achieved for all devices. To reach , a larger gate voltage swing is required, which increases the gate leakage and with possible risk of dielectric breakdown. The corresponding gate leakage for device #1, for which the NF measurement was performed, was pA, which eliminates the shot noise and noise in FET resistive mixers [23]. The small shift of the Dirac voltage is beneficial for the mixer to operate at zero gate bias. The asymmetry around is also small, which is important for the subharmonic mixing capability.

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TABLE II MEASURED IIP3 AT

AND

dBm

AND

GHz

TABLE III MEASURED IIP3 AT

Fig. 4. Corresponding resistance swept by the LO in mixer operation for the V, together with the modeled resistance curves used in devices at the simulations. TABLE I SUMMARY OF DEVICE PARAMETERS USED FOR SIMULATIONS

order to be measured, but still the result is sensitive to imperfections in the setup. The error is mainly attributed to mismatch at the drain, which is approximately equal at and due to the low frequency. Harmonic-balance simulations using the large-signal model in [21] predicts the RF and IF impedances presented by the mixer to be 100 , which yields with . Despite the measurement uncertainty, there is clearly a close correlation between the CL and NF, . This relation between the CL and NF was analyzed with the attenuator noise model for passive mixers [23]. For an FET resistive mixer, in the absence of gate leakage current, the noise is generally entirely thermal. The model establishes that, under these conditions, the noise temperature is dependent only upon the CL, assumed to be for both sidebands, and physical temperature, , as (5) In the ideal case where both RF and image sidebands are down-converted with the same CL, it is valid that . The definition of the NF for mixers is ambiguous, although the most relevant relation to noise temperature is given by

Fig. 5. CL and SSB NF of the device #1 G-FET resistive mixer versus RF frequency. The measurement is performed at room temperature. The error bars correspond to 2 dB and 1 dB, respectively.

A. Mixer NF The resulting CL and NF for the mixer, given by device #1, in the frequency range – GHz are shown in Fig. 5 as measured by the NFA. The CL lies in the interval 20–22 dB 1 dB and was verified at GHz using a spectrum analyzer. The high CL is limited by the uneven distribution in time of and and the waveform shape. This requires a higher on–off ratio to reach the same performance as conventional fundamental resistive FET mixers [16]. Due to the thin gate dielectric, the required LO power was merely dBm, a significant improvement to dBm in [12]. The operating frequency interval corresponds to the best reported G-FET mixers, while the CL represents a state-of-the-art result [11], [12], [24]. The NF presented in Fig. 5 is single-sideband (SSB) after applying a 3-dB correction to the measured DSB quantity, which is valid as outlined in the analysis of the mixer NF below. The SSB NF is greater than the CL by 1 dB, with an estimated measurement accuracy of 2 dB according to the investigation in [25]. At this high CL, the accompanying NF must be high in

(6) K, is that it preThe main benefit of (6), where serves the relation from SSB and DSB noise temperatures such that , as utilized above to convert the NF from DSB to SSB. At room temperature, where , inserting (5) into (6) finally translates into . The result of Fig. 5 is thus a confirmation of the noise to be essentially thermal in a G-FET resistive mixer, true for example, for a GaAs fundamental resistive mixer [26] and CMOS subharmonic resistive mixer [27]. Hence, an evident approach to improve the NF is to reduce the CL, as for every passive mixer. It should also be possible to cool the mixer to low temperatures, with a greater improvement as compared, for example, to Schottky mixer diodes, which are then limited by shot noise [28]. A -factor measurement with a combination of high loss and low NF would, though, result in an unacceptable uncertainty and was therefore not conducted at this stage. B. Mixer Intermodulation The two-tone measurements for device #2 are summarized in Tables II and III versus RF frequency and LO pump power level. Results for device #2 at 2 GHz are presented in Fig. 6 with the

ANDERSSON et al.: RESISTIVE G-FET SUBHARMONIC MIXERS

Fig. 6. Linear and third-order response for device #2 at 2 GHz, and dBm with dBm.

TABLE IV COMPARISON OF THE G-FET SUBHARMONIC MIXER WITH FUNDAMENTAL SINGLE-ENDED RESISTIVE MIXERS

linear and third-order responses (error 0.5 dB for both). To deduce the third-order intercept point, the regression analysis enforces a slope of one for the linear response and a slope of three for the third-order response. The highest measured value for the G-FET subharmonic resistive mixer is dBm at dBm at GHz. Although it is possible to have single-device balanced designs [29], the comparison to earlier work considers single-ended fundamental resistive FET mixers, as presented in Table IV. On one side, for high power-handling GaN and SiC FETs [30], [31], IIP3 values in excess of 30 dBm have been reported. These, however, come at the expense of 23–27-dBm LO power. On the other hand, in CMOS, IIP3 of 16.5 dBm has been achieved with 4-dBm LO power [32]. In between, GaAs single-ended resistive mixers achieve dBm with dBm [26]. Another way of comparing is the use of the IIP3 quality factor, , also shown in Table IV. For our G-FET mixer, the maximum dB from Table II. Further, the comparison of IIP3 to subharmonic FET resistive mixers (although more seldom reported in the literature) has to consider more complex design architectures since the singleended subharmonic mixer is a novel G-FET concept. The IMD is generally worse, for example, with a single-balanced CMOS mixer reaches dBm and dB at a CL of 12 dB [27]. In order to evaluate the IMD results, two-tone harmonic-balance simulations were conducted with the large-signal model presented in [21]. The gate bias voltage was varied and the measured and simulated linear and third-order responses were compared. The results at are compared in Fig. 7. This was performed for device #3, which exhibited a symmetric transfer characteristic, and therefore only one branch was considered. The measured and simulated results for IIP3 are given

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Fig. 7. Measured and modeled linear and third-order response for device #3 at and dBm. 2 GHz,

TABLE V COMPARISON BETWEEN MEASURED AND SIMULATED IIP3 DEVICE #3 AT GHz AND dBm

FOR

TABLE VI COMPARISON BETWEEN MEASURED AND SIMULATED CL FOR DEVICE #3 AT GHz AND dBm

in Table V. A slightly higher value of dBm was used for this measurement to provide a comparable , despite the lower mobilities (compare Table I). Clearly, at the results from the model are in excellent agreement with measurements. On the other hand, away from the Dirac voltage, the model tends to overestimate the third-order IMD response, leading to a lower IIP3 point. A complete linear response comparison, showing the rapidly increasing CL with a bias deviating from the Dirac voltage, is presented in Table VI, with good agreement. The discrepancy that exists is partly attributed to an error in the estimated losses in the RF and IF paths of the measurement setup. These results are in line with similar HEMT/MESFET models [33]. To improve the IIP3 of future G-FET resistive mixers, operation at higher LO power is preferred, as observed in the literature for resistive mixers, the trend in Table III, as well as in Section VI. Conventional FET resistive mixers biased at zero drain voltage also operate in a linear regime in gate–source voltage. The introduction of the resistive mixer was partly motivated by the fact that a time-varying linear element can also be used for mixing [26] with improved intermodulation performance. This can be understood by describing the output voltage as a general nonlinear network in terms of a Taylor series in input voltage (7)

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Fig. 8. Modeled IIP3 versus and at the Dirac voltage Measured performance in this study is circled.

.

Fig. 9. Modeled CL versus and at the Dirac voltage Measured performance in this study is circled.

.

Fig. 10. Modeled versus and at the Dirac voltage Measured performance in this study is circled.

.

With a two-tune input at frequencies and , the cubed term of (7) results in the harmful third-order intermodulation products and , which are virtually impossible to filter out. By the use of a linear mixing network, these frequency products can be suppressed. The current G-FET resistive mixers, though, have an shape for each branch that is not linear, but instead saturates at higher gate bias as limited by the parasitic resistances. To make the resistance for each branch more linear, a decrease of the parasitic resistances is thus an important step. This is further discussed in Section VI. C. Discussion About Mixer CL The reduction of contact and access resistances also helps to reduce , especially since it yields (typically 50 ) to make . To improve the CL for the resistive mixer application, the introduction of a bandgap in single-layer graphene is not crucial for the purpose of achieving current saturation in the G-FET. Instead, it is important to have to make and also so that the on and off states can have a more equal duration in time. Together these steps will make resemble a 0.5 duty-cycle square wave and help minimize the CL. Moreover, lower contact and access resistances and the introduction of a bandgap would improve the device transconductance. This makes it more suitable for transconductance mixing with the prospect of achieving higher conversion gain in future G-FET mixers. In this context, increased mobility is of course an important step toward improved performance. VI. FUTURE PERFORMANCE PREDICTION In order to predict the possible future performance of the G-FET subharmonic mixer, simulations were performed when biased at the Dirac voltage for optimum CL. The model confirms that higher LO power is a general route to improved IIP3, as seen from Fig. 8. In order to reduce the demands on LO power, increased mobilities are essential for a steeper transfer characteristic to change from to with a smaller voltage swing. Furthermore, concerning a lowered

contact resistance, , the results from the simulations partly contradict the claim of Section V-B, which is attributed to a simultaneously improved CL, as presented in Fig. 9. This yields higher amplitudes for the down-converted signals at frequencies and , and consequently higher power, , for the third-order intermodulation products. The results on the CL also translate to the NF due to the thermal noise with . Finally, combining the simulated IIP3 and CL data, the mixer spurious-free dynamic range (up to the , where reaches the noise floor) is calculated [34] according to (8), assuming unity signal-to-noise ratio (SNR) at the mixer output, and presented in Fig. 10. In (8), is the output noise power assuming a MHz. The performance of the devices presented in this study, with good agreement between experimental and simulated results, is circled in Figs. 8–10 with a current dB. From Fig. 10, this can be improved significantly at higher LO power. Operation at higher LO power, though, requires an improved gate–oxide quality to prevent gate current conduction (8)

ANDERSSON et al.: RESISTIVE G-FET SUBHARMONIC MIXERS

VII. CONCLUSION The first NF measurement and IMD analysis of a subharmonic resistive G-FET mixer have been conducted and reported. The devices exhibit state-of-the-art performance for graphene-based mixers concerning LO power requirement and CL. The noise was determined to be essentially thermal. Future low-temperature experiments will clarify possible departure from thermal noise. Nevertheless, it is important to address the issue of high CL to realize a practical G-FET mixer, e.g., for receiver sensitivity. Accomplishing a lower CL of the mixer includes an increased on–off ratio, by decreasing parasitic resistances and introducing a bandgap in graphene, as well as devices operating at higher LO power. The latter makes the subharmonic mixer operation more linear to keep the IIP3 advantage of resistive mixers to active mixers. A bandgap formation helps to have, for lower CL, a beneficial shape of . If these important steps can be achieved, the G-FET resistive subharmonic mixer can be competitive with CMOS counterparts concerning both performance and cost. ACKNOWLEDGMENT The authors would like to thank N. Wadefalk, Chalmers University of Technology, Göteborg, Sweden, for help with the NF measurements and Prof. E. Kollberg and and R. Dahlbäck, both with Chalmers University of Technology, for useful input on this paper’s manuscript. REFERENCES [1] S. Cha, J. H. Choi, C. W. Baik, H. B. Sohn, J. Choi, O. Kim, and J. M. Kim, “Perspectives on nanotechnology for RF and terahertz electronics,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 10, pp. 2709–2718, Oct. 2011. [2] S. O. Koswatta, A. Valdes-Garcia, M. B. Steiner, Y.-M. Lin, and P. Avouris, “Ultimate RF performance potential of carbon electronics,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 10, pp. 2739–2750, Oct. 2011. [3] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science, vol. 306, no. 5659, pp. 666–669, Oct. 2004. [4] J.-S. Moon and D. K. Gaskill, “Graphene: Its fundamentals to future applications,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 10, pp. 2702–2708, Oct. 2011. [5] F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nature Photon., vol. 4, pp. 611–612, Aug. 2010. [6] F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nature Mater., vol. 6, pp. 652–655, Jul. 2007. [7] M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Lett., vol. 28, no. 4, pp. 282–284, Apr. 2007. [8] Y. Q. Wu, D. B. Farmer, A. Valdes-Garcia, W. J. Zhu, K. A. Jenkins, C. Dimitrakopoulos, P. Avouris, and Y.-M. Lin, “Record high RF performance for epitaxial graphene transistor,” in IEEE Int. Devices Meeting, Dec. 2011, pp. 23.8.1–23.8.3. [9] H. Wang, A. Hsu, J. Wu, J. Kong, and T. Palacios, “Graphene frequency multipliers,” IEEE Electron Device Lett., vol. 30, no. 5, pp. 547–549, May 2009. [10] H. Wang, A. Hsu, J. Wu, J. Kong, and T. Palacios, “Graphene-based ambipolar RF mixers,” IEEE Electron Device Lett., vol. 31, no. 9, pp. 906–908, Sep. 2010.

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[11] Y.-M. Lin, A. Valdes-Garcia, S. Han, D. B. Farmer, I. Meric, Y. Sun, Y. Wu, C. Dimitrakopoulos, A. Grill, P. Avouris, and K. A. Jenkins, “Wafer-scale graphene integrated circuit,” Science, vol. 332, no. 6035, pp. 1294–1297, Jun. 2011. [12] O. Habibpour, S. Cherednichenko, J. Vukusic, K. Yhland, and J. Stake, “A subharmonic graphene FET mixer,” IEEE Electron Device Lett., vol. 33, no. 1, pp. 71–73, Jan. 2012. [13] M. A. Andersson, O. Habibpour, J. Vukusic, and J. Stake, “A 10-dB small-signal graphene FET amplifier,” Electron. Lett., vol. 48, no. 14, pp. 861–863, Jul. 2012. [14] G. Deligiorgis, F. Coccetti, G. Konstantinidis, and R. Plana, “Radio frequency signal detection by ballistic transport in Y-shaped graphene nanoribbons,” Appl. Phys. Lett., vol. 101, pp. 013 502–013 502, 2012. [15] S. A. Maas, Nonlinear Microwave and RF Circuits. Norwood, MA: Artech House, 2005. [16] K. Yhland, “Simplified analysis of resistive mixers,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 8, pp. 604–606, Aug. 2007. [17] A. J. Kelly, “Fundamental limits on conversion loss of double sideband resistive mixers,” IEEE Trans. Microw. Theory Techn., vol. MTT-25, no. 11, pp. 867–869, Nov. 1977. [18] H. Zirath, “Subharmonically pumped resistive dual-HEMT-mixer,” in IEEE MTT-S Int. Microw. Symp. Dig., Jul. 1991, pp. 875–878. [19] M. Andersson, O. Habibpour, J. Vukusic, and J. Stake, “Noise figure characterization of a subharmonic graphene FET mixer,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [20] J. S. Moon, D. Curtis, D. Zehnder, S. Kim, D. K. Gaskill, G. G. Jernigan, R. L. Myers-Ward, C. R. Eddy, P. M. Campbell, K.-M. Lee, and P. Asbeck, “Low-phase-noise graphene FETs in ambipolar RF applications,” IEEE Electron Device Lett., vol. 32, no. 3, pp. 270–272, Mar. 2011. [21] O. Habibpour, J. Vukusic, and J. Stake, “A large signal graphene FET model,” IEEE Trans. Electron Devices, vol. 59, no. 4, pp. 968–975, Apr. 2012. [22] R. A. Pucel, D. Masse, and R. Bera, “Performance of GaAs MESFET mixers at band,” IEEE Trans. Microw. Theory Techn., vol. MTT-24, no. 6, pp. 351–360, Jun. 1976. [23] S. A. Maas, Noise in Linear and Nonlinear Circuits. Norwood, MA: Artech House, 2005. [24] L. Liao, J. Bai, R. Cheng, H. Zhou, L. Liu, Y. Liu, Y. Huang, and X. Duan, “Scalable fabrication of self-aligned graphene transistors and circuits on glass,” Nano Lett., vol. 12, no. 6, pp. 2653–2657, Jun. 2011. [25] “Noise figure measurement accuracy—The -factor method,” Agilent Technol., Santa Clara, CA, Agilent Appl. Note, 2010, pp. 57–62. [26] S. A. Maas, “A GaAs MESFET mixer with very low intermodulation,” IEEE Trans. Microw. Theory Techn., vol. MTT-35, no. 4, pp. 425–429, Apr. 1987. [27] H.-J. Wei, C. Meng, P.-Y. Wul, and K.-C. Tsung, “ -band CMOS sub-harmonic resistive mixer with a miniature marchand balun on lossy silicon substrate,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 1, pp. 40–42, Jan. 2008. [28] A. van der Ziel, “Theory of shot noise in junction diodes and junction transistors,” Proc. IRE, vol. 43, no. 11, pp. 1639–1646, Nov. 1955. [29] K. Yhland, N. Rorsman, and H. Zirath, “Novel single device balanced resistive HEMT mixers,” IEEE Trans. Microw. Theory Techn., vol. 43, no. 12, pp. 2863–2867, Dec. 1995. [30] M. Sudow, K. Andersson, M. Fagerlind, M. Thorsell, P.-A. Nilsson, -band AlGaN/GaN and N. Rorsman, “A single-ended resistive HEMT MMIC mixer,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 10, pp. 2201–2206, Oct. 2008. [31] K. Andersson, J. Eriksson, N. Rorsman, and H. Zirath, “Resistive SiCMESFET mixer,” IEEE Microw. Wireless Compon. Lett., vol. 12, no. 4, pp. 119–121, Apr. 2002. [32] B. M. Motlagh, S. E. Gunnarsson, M. Ferndahl, and H. Zirath, “Fully integrated 60-GHz single-ended resistive mixer in 90-nm CMOS technology,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 1, pp. 25–27, Jan. 2006. [33] K. Yhland, N. Rorsman, M. Garcia, and H. F. Merkel, “A symmetrical nonlinear HFET/MESFET model suitable for intermodulation analysis of amplifiers and resistive mixers,” IEEE Trans. Microw. Theory Techn., vol. 48, no. 1, pp. 15–22, Jan. 2000. [34] D. M. Pozar, Microwave and RF Design of Wireless Systems. New York: Wiley, 2001.

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Michael A. Andersson (S’12) was born in Varberg, Sweden, in 1988. He received the B.S. and M.Sc. degrees in electrical engineering from the Chalmers University of Technology, Göteborg, Sweden, in 2010 and 2012, respectively, and is currently working toward the Ph.D. degree in graphene electronics for high-frequency applications at the Chalmers University of Technology. He is currently with the Terahertz and Millimetre Wave Laboratory, Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology.

Omid Habibpour (S’08) received the B.S. degree in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 2002, the M.S. degree in electrical engineering from the Amirkabir University of technology, Tehran, Iran, in 2004, and is currently working toward the Ph.D. degree in graphene electronics at the Chalmers University of Technology, Göteborg, Sweden. He is currently with the Terahertz and Millimetre Wave Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology.

Josip Vukusic (M’11) received the Diploma degree and Ph.D. degree in photonics from the Chalmers University of Technology, Göteborg, Sweden, in 1997 and 2003, respectively. Since 2004, he has been with the Terahertz and Millimetre Wave Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, where he is involved with terahertz technology. He is currently involved in modeling, fabrication, and characterization of frequency multipliers for terahertz generation.

Jan Stake (S’95–M’00–SM’06) was born in Uddevalla, Sweden, in 1971. He received the M.Sc. degree in electrical engineering and Ph.D. degree in microwave electronics from the Chalmers University of Technology, Göteborg, Sweden in 1994 and 1999, respectively. In 1997, he was a Research Assistant with the University of Virginia, Charlottesville. From 1999 to 2001, he was a Research Fellow with the Millimetre Wave Group, Rutherford Appleton Laboratory, Didcot, U.K. He then joined Saab Combitech Systems AB, where he was a Senior RF/Microwave Engineer until 2003. From 2000 to 2006, he held different academic positions with the Chalmers University of Technology, and from 2003 to 2006, was also Head of the Nanofabrication Laboratory, Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology. During Summer 2007, he was a Visiting Professor with the Submillimeter Wave Advanced Technology (SWAT) Group, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena. He is currently a Professor and Head of the Terahertz and Millimetre Wave Laboratory, Department of Microtechnology and Nanoscience (MC2). He is also cofounder of Wasa Millimeter Wave AB, Göteborg, Sweden. His research involves sources and detectors for terahertz frequencies, high-frequency semiconductor devices, graphene electronics, and terahertz measurement techniques and applications. Prof. Stake is a topical editor for the IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY.

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High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers Michael Roberg, Student Member, IEEE, Tibault Reveyrand, Member, IEEE, Ignacio Ramos, Student Member, IEEE, Erez Avigdor Falkenstein, Student Member, IEEE, and Zoya Popović, Fellow, IEEE

Abstract—This paper presents a theoretical analysis of harmonically terminated high-efficiency power rectifiers and experimental validation on a class-C single Schottky-diode rectifier and a class-F GaN transistor rectifier. The theory is based on a Fourier analysis of current and voltage waveforms, which arise across the rectifying element when different harmonic terminations are presented at its terminals. An analogy to harmonically terminated power amplifier (PA) theory is discussed. From the analysis, one can obtain an optimal value for the dc load given the RF circuit design. An upper limit on rectifier efficiency is derived for each case as a function of the device on-resistance. Measured results from fundamental frequency source–pull measurement of a Schottky diode rectifier with short-circuit terminations at the second and third harmonics are presented. A maximal device rectification efficiency of 72.8% at 2.45 GHz matches the theoretical prediction. A 2.14-GHz GaN HEMT rectifier is designed based on a class-F PA. The gate of the transistor is terminated in an optimal impedance for self-synchronous rectification. Measurements of conversion efficiency and output dc voltage for varying gate RF impedance, dc load, and gate bias are shown with varying input RF power at the drain. The rectifier demonstrates an efficiency of 85% for a 10-W input RF power at the transistor drain with a dc voltage of 30 V across a 98- resistor. Index Terms—Harmonic terminations, high-efficiency power amplifiers (PAs), load–pull, microwave rectifiers, nonlinear analysis, time-domain measurements.

T

I. INTRODUCTION

HE FIRST RF rectifiers were demonstrated in experiments and patents in the 1890s by Nikola Tesla in wireless power transmission for lighting applications and the method of obtaining direct from alternating current [1]. The

Manuscript received July 09, 2012; revised September 23, 2012; accepted September 25, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported in part by the Office of Naval Research (ONR) under the Defense Advanced Research Projects Agency (DARPA) Microscale Power Conversion (MPC) Program under Grant N00014-11-1-0931, and in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy under Award Number DE-AR0000216. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. . M. Roberg is with TriQuint Semiconductor, Richardson, TX 75080 USA (e-mail: [email protected]). T. Reveyrand is with the XLIM Laboratory, UMR 7252, University of Limoges, 87060 Limoges, France (e-mail: [email protected]). I. Ramos and Z. Popović are with the Department of Electrical, Computer and Energy Engineering, University of Colorado at Boulder, Boulder, CO 80309-0425 USA (e-mail: [email protected]; [email protected]). E. A. Falkenstein is with Qualcomm Inc., Boulder, CO 80301 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222919

main application of microwave power rectifiers in the early 1900s was in signal detection where crystals, vacuum tubes, or diodes served as the nonlinear element [2], [3]. An excellent discussion of the early history of microwave detectors is provided in [4]. These early microwave rectifiers were aimed at extracting information rather than extracting dc power. The first published application of microwave rectifiers for extraction of dc power was performed in the 1960s using diode-based rectifiers [5]–[8]. Renewed interest in free-space power transmission occurred in the early 1970s. An interesting microwave rectifier for production of dc power or low-frequency ac power called the cyclotron-wave rectifier was introduced in [9] and [10]. William C. Brown, Raytheon, Boston, MA, one of the original researchers in the field, continued publishing diode-based rectifier work and introduced the term “rectenna” for a receiving antenna integrated with a rectifier [11]–[13]. Around the same time, power combining for an array of microwave power rectifiers was discussed in [14], in which the authors inadvertently graze the topic of harmonically terminated rectifiers, of which they seem to hint at a class-F rectifier. A number of diode-based rectifiers have been demonstrated, many integrated with antennas, with a good comparison presented in [15] and in earlier works focusing on low-power rectification [16], [17]. Additional applications where rectifier efficiency is important include microwave power recycling [18], and dc–dc converters with extremely high-frequency switching [19], [20]. In many of the reported microwave rectifiers, filtering of the harmonics at both the input and output has been investigated, e.g., [21] and [22], mainly to reduce re-radiated harmonic power. To date, very few transistor rectifier circuits have been demonstrated, most at frequencies at least three times lower than in this study. A UHF synchronous transistor class-E rectifier at 700 MHz is shown to achieve 85% efficiency with 58 mW of output power in [20], and the same authors discuss 10-W dc–dc converter with a synchrounous trana classsistor rectifier at 780 MHz with 72% efficiency [23]. This design is scaled from 0.5-MHz synchronous rectifier designs demonstrated in [24] and requires an additional synchronized gate RF input signal. Harmonic terminations are commonly applied to increase efficiency in power amplifiers (PAs). The transistor nonlinearities generate harmonic content at the output, and in a number of high-efficiency amplifier classes, specific harmonic terminations are used to shape the current and voltage waveforms. In reduced conduction angle PAs (classes A, AB, B, and C), all harmonics are shorted at the virtual drain reference plane in the transistor. Other PA modes of operation specify open or short

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Fig. 1. Microwave rectifier circuit diagram. An ideal blocking capacitor provides dc isolation between the microwave source and rectifying element. An isolates the dc load from RF power. ideal choke inductor

harmonic terminations for various harmonics [25]–[27]. A general analysis for arbitrary complex terminations of harmonics have recently been derived in [28], including a sensitivity analysis to harmonic termination impedances. In a rectifier, the nonlinear rectifying element also generates currents and voltages at the harmonics of the input frequency, and although in this case the output is at dc, the efficiency of the rectifier can be modified by terminating the harmonics. In [29], the harmonic termination concept for improving rectifier efficiency is applied to a class-C diode rectifier integrated with a dual-polarized patch antenna for a wireless powering application. In this paper, we identify the similarity between power rectifiers and PAs, showing that many of the efficiency improvement techniques developed for PAs may be practically directly applied to power rectifiers. Particularly, the impact that harmonic terminations have on the rectification efficiency is addressed. A general rectifier analysis approach is presented in Section II, and several classes of microwave power rectifiers are introduced, focusing on class-C and F modes, which are experimentally validated in Sections III and IV. II. HARMONICALLY TERMINATED POWER-RECTIFIER ANALYSIS Consider the microwave rectifier shown in Fig. 1. A sinusoidal microwave power source with voltage magnitude and impedance drives the rectifying element having a resistance defined as (1) where and are the instantaneous voltage across and current through the rectifying element, respectively. The rectifying element depicted by in Fig. 1 can, in general, be any nonlinear device that acts as a switch, such as a diode or a transistor. When a nonzero on-resistance and nonzero threshold voltage are taken into account, the resistance of the rectifying element is given by (2) The analysis of different classes of power rectifiers will be analyzed next based on the harmonic terminations presented to the rectifying element, and independent of the physical nonlinear device, which performs the rectification. A. Class-C Rectifier Analysis In Fig. 1, a sinusoidal microwave power source with voltage magnitude and impedance drives the rectifying element

of resistance above. The dc load seen by the rectifying element is , while the load at the fundamental frequency and successive harmonics is set by the matching network. Assume the matching circuit presents to the rectifying element with all subsequent harmonics terminated in short circuits. This is equivalent to the harmonic terminations for a canonical reduced conduction angle PA. This class is useful for Schottky diode rectifiers because these diodes have nonlinear junction capacitance. Short circuiting the harmonics fixes the harmonic terminations at the intrinsic diode by shorting this junction capacitance. When the incident RF voltage at the ideal rectifier swings negative, it is clipped at zero given (1). The enforced harmonic terminations force the voltage waveform to contain only a dc and fundamental frequency component. Therefore, a dc component must be produced by the rectifying element such that the voltage waveform maintains its sinusoidal nature. The voltage across the rectifying element can now be expressed as (3) is the fundamental frequency component of the where voltage across the rectifying element, is the dc component, , and . The current waveform contains infinite frequency components, and can be written as

(4) where is the dc current and is the Dirac delta function. When all available input power is delivered to the rectifier, the fundamental frequency component of the current through the rectifying element is (5) and, since there is no mechanism by which the rectifier itself can dissipate power ( at this point), all of the available input power must be dissipated in the dc load and the conversion efficiency is 100%. Therefore, (6) Substituting in (5) and rearranging gives the expression of the current at the fundamental input frequency and the dc rectified current, which is . When all available input power is delivered to the rectifier, the RF–dc conversion efficiency is 100% because the rectifying element is ideal and cannot dissipate power itself. In order for all available input power to be delivered to the rectifier, it is straightforward to show that the dc load must be set relative to the fundamental frequency load as (7) A harmonic-balance simulation of an approximately ideal rectifier with short-circuited harmonic terminations was performed in Microwave Office using the SPICE diode model with no parasitics (PNIV) as the rectifying element. The device temperature was set to 1 K to approximate an ideal switch. The

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harmonic terminations is the same as for a class-F amplifier, therefore this rectifier will be referred to as a class-F rectifier. The fundamental frequency component of the voltage across the rectifying device is given by (9) During the second half of the RF cycle, it is evident from (1) that the voltage across the rectifying element must be zero. This condition must be met through the addition of dc and only even harmonic voltage components, and therefore the voltage waveform is expressed as (10) Fig. 2. Ideal normalized voltage (dashed) and current (solid) waveforms for reduced conduction angle half-wave rectifier. The waveforms have been normalized to their peak values.

A Fourier expansion of (10) expresses the dc component of the voltage waveform as (11) In the first half of the RF cycle, the current through the rectifying element is zero, given (1). This condition is met through the addition of a dc current and odd harmonic current components. With the current direction as in Fig. 1, the dc component of the current must be positive. Therefore, in the first half of the RF cycle, the remaining harmonics must sum to a constant value equivalent to the negative of the dc component. Since the function, which is the sum of the remaining harmonics is odd, the second half of the RF cycle must sum to the dc component, and the current is given by (12)

Fig. 3. Simulated efficiency of reduced conduction angle half-wave rectifier for varying rectifier on-resistance. versus

The dc component of the current waveform Fourier expansion is found to be fundamental frequency excitation was set to 1 W at 1 GHz with the first 200 harmonics terminated in short circuits. The diode was presented with 50 at the fundamental frequency and the dc load was swept from 5 to 200 . The simulated data is then normalized to generalize the simulation results. The ideal time-domain current and voltage waveforms across the diode are shown in Fig. 2 with the RF–dc conversion efficiency as a function of for varying rectifier on-resistance shown in Fig. 3. It is clear that the mechanism of operation in the ideal case agrees with the theory presented above. The reduction in RF–dc conversion efficiency when the dc load is not set according to (7) is due to impedance mismatch, and is given by

(8)

B. Class-F

Rectifier Analysis

Consider again the rectifier circuit shown in Fig. 1 and assume that all even harmonics are terminated in open circuits, while all odd harmonics are terminated in short circuits. This set of

(13) The dc load consistent with (10) and (12) is given by (14) The conversion efficiency, defined as the ratio of the dc power dissipated in the load resistor to the available fundamental frequency RF power, is evaluated as (15) Therefore, the ideal half-wave rectifier converts all available RF power to dc power if the dc loading resistance is set to the value given in (14). The RF–dc conversion efficiency as a function of was simulated in Microwave Office for varying rectifier on-resistance and is shown in Fig. 4. The harmonic-balance settings were identical to those used for the class-C rectifier above. The peak efficiency as a function of on-resistance is higher than for the class-C rectifier, although the efficiency degrades more quickly when the nonideal dc load is applied.

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The dc and fundamental frequency values of the voltage and current waveforms can be found through a Fourier analysis using the transition points in (18). The first Fourier coefficient of gives the dc component of the voltage, which can be derived as

(19) The fundamental frequency voltage is found from , where Fig. 4. Simulated efficiency of class-F varying rectifier on-resistance.

rectifier versus

for

(20) and

can be reduced to

(21) Similarly, the dc component of the current waveform is found to be (22) Fig. 5. Nonideal class-F voltage (solid) and current (dashed) waveforms, normalized to their peak respective values.

The waveforms including parasitic on-resistance and threshold voltage are next investigated assuming the rectifier impedance from (2). The time-domain voltage and current waveforms are approximated as (16)

The fundamental frequency current and the coefficient can be shown to be equal to

has

(23) The input power at the fundamental frequency is found from (24) Substituting (21) and (23) into the above results in

(17) As an example, Fig. 5 shows the current and voltage waveV, forms for a specific set of nonideal parameters ( V, mA, and ). When the device is conducting current, it creates a voltage drop across the on-resistance, which is constant due to the constant current. If the on-resistance were zero, the only difference between the waveform in (16) and the ideal voltage waveform would be the minimum value, which would be rather than zero. The values of at which the transition between the conducting and nonconducting regions occurs are found to be

(25) where

is defined as (26)

as a function of when is nonzero Solving for after some arithmetic results in two solutions, one of which is negative. The positive solution for the maximal current is (27)

(18)

with

.

ROBERG et al.: HIGH-EFFICIENCY HARMONICALLY TERMINATED DIODE AND TRANSISTOR RECTIFIERS

In the case where

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is zero, (27) simplifies to (28)

Note that in the case of an ideal rectifying element, and , therefore, (29) Now that is fully expressed given known rectifier parameters, and , and may be calculated, and from this, the dc load and the load at fundamental frequency determined from the following expressions: (30)

Fig. 6. Source–pull contours with available input power to the diode set to 6 dBm. The impedance is referenced to the junction capacitance of the diode, therefore the lead inductance of the package has been compensated for. Setting to 1080 was found to result in the optimal efficiency for this input power. with The highest efficiency of 77.6% is obtained at V.

(31) The negative impedance in (31) indicates that power is delivered to the rectifying element and gives the impedance of the source delivering power to the rectifying element. The rectifier efficiency is given by (32)

C. Design Example Based on Class-F

Theory

To understand the usefulness of the presented theory, assume the rectifying element has the following parameters: V, , V, and W. First, (27) is used to calculate mA. Next, the dc voltage and current are evaluated using (19) and (22), respectively, to give V and mA. The fundamental frequency voltage and current Fourier coefficients are then calculated to be V and mA, respectively. The dc and fundamental frequency resistances are then calculated using (30) and (31) to be and , respectively. The efficiency is then calculated using (32) to be . If the input power is selected as 0.1 W rather than 1 W, the resulting efficiency is 72.43%. A specific rectification device will always have an approximate input drive level at which it can be most efficient, just as with power transistors in PAs. To maximize efficiency, the goal is always to minimize the amount of power dissipation in the on-resistance of the rectifying element and maximize the power dissipated in the dc load resistor. III. SCHOTTKY-DIODE CLASS-C RECTIFIER The Skyworks SMS7630 Schottky diode in the SC-79 package was selected for the half-wave rectifier. Source–pull was performed at 2.45 GHz with 0–10 dBm available input power for various dc loads in order to identify the combination of input power, fundamental load, and dc load resulting in highest efficiency. The best case occurred at 6-dBm input

Fig. 7. RF–dc conversion efficiency versus dc load for fixed available input powers with 0.6-dB matching network loss de-embedded. The maximum effiand V, ciency of 72.8% occurred at 8 dBm with which is lower than the 1080 found during source–pull. However, the efficiency at 1080 is 69.9% which is very close to the peak value.

power with the source–pull contours shown in Fig. 6. The on-resistance of the SMS7630 is 20 with the optimal dc load of 1080 . Therefore, is approximately 2% of , which, in theory, is 4% of . From Fig. 3, a peak efficiency of 87% occurs with infinite harmonic terminations, therefore the achieved 77.6% is very reasonable considering only the second and third harmonics were explicitly terminated. Measurements of a rectifier designed using the source–pull data show a maximum RF–dc conversion efficiency of 72.8% when matched to 50 , obtained after the 0.6-dB matching network loss is de-embedded. The fabricated rectifier and dc load sweep measurements are shown in Fig. 7. Open-circuit shunt stubs are used to present short-circuit terminations at the second and third harmonics. A shunt capacitor is used for presenting the fundamental frequency impedance to reduce size and allow tunability. The reduction in efficiency relative to the source–pull measurements is due to the matching circuit not presenting the ideal impedance found during source–pull.

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Fig. 9. Large-signal measurements performed on the class-F GHz, V, and V. Fig. 8. Photograph of the class-F in [30].

PA at

PA, working at 2.14 GHz and presented

The class-C rectifier can be applied to improving the efficiency of a wireless powering reception device, as demonstrated in [29], with a dual-linearly polarized patch rectenna, with a rectifier circuit for each polarization. In this circuit, the first five harmonics are shorted and the impedances are validated by calibrated measurements and are presented in [29]. IV. TRANSISTOR CLASS-F

RECTIFIER

To prove experimentally the duality between harmonically terminated PAs and rectifiers, a high-efficiency class-F PA was designed, measured first as an amplifier, and then as a rectifier. In the rectifier measurements, RF power is input into the drain, which is unbiased. The gate is terminated in a variable impedance and biased close to pinch-off. Measurements of efficiency and dc voltage are performed in the time domain as a function of input RF power, gate RF load, gate bias, and drain dc load. A. Circuit Design A 2.14-GHz PA, shown in Fig. 8, is designed using the Triquint TGF2023-02 GaN HEMT [30]. Class F harmonic terminations are implemented at the second and third harmonics. The performance of the PA, illustrated in Fig. 9, was characterized at 2.14 GHz with a drain voltage bias of 28 V and a bias current of 160 mA. The PA exhibits a power-added efficiency (PAE) of 84% with an output power of 37.6 dBm and a gain of 15.7 dB under 3-dB compression. The same PA design was used for rectifier measurements, as shown in Fig. 10. The PA is connected to an input RF source at the drain with the drain supply disconnected. The gate terminal is biased, and connected to an impedance tuner, converting the two-port transistor PA to a one-port rectifier, corresponding to the generalized schematic of Fig. 1. B. Measurement Setup The class-F PA described above is fully characterized in large signal in a rectifier configuration with the setup shown

Fig. 10. Time-domain nonlinear rectifier measurement block diagram. The SWAP [31] performs sampling of current and voltage and the calibration refers the sampled quantities to the reference planes at the DUT. The drain output dc , the gate bias , and the gate RF impedance are varied resistance as the input power at the drain is swept from 10 to 42 dBm.

in Fig. 10. The commercial time-domain large-signal measurement instrument is a VTD SWAP four-channel receiver [31]. In order to acquire time-domain waveforms at the reference plane, an eight-error term model calibration similar to the one performed for large-signal network analyzer (LSNA) measurements is applied. After an absolute vector network analyzer (VNA)-like calibration [32], the RF voltage and current waveforms at the input (V1 and I1) and at the output (V2 and I2) of the device-under-test (DUT) are measured at the coaxial reference plane. In this case, the RF input is the drain port of the PA, while the RF output is connected to the gate port. Thus, performing a load–pull on this device consists of varying the load at at the RF gate port of the PA with a passive tuner. This kind of measurement is similar to large-signal characterization of switch devices recently reported in [33] and [34]. The gate dc path is connected to a power supply so the gate bias can be varied. The drain dc bias is the output of the rectifier and is connected to a variable resistance , and the dc voltage across it is measured with a voltmeter. The dc current is then found from the value of from (30). During the measurement, several parameters are varied systematically: the RF load impedance applied at the PA gate port ; the resistor in the dc drain output ; and the gate bias voltage .

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Fig. 11. Time-domain waveforms measured at: (a) drain and (b) gate of the V, , and . rectifier with The RF input power at the drain is swept from 10 to 42 dBm, corresponding to the range of output power of the class-F PA.

The conversion efficiency of the rectifier and the dc power delivered at the drain output of the rectifier are measured as these parameters are varied, and as a function of input power at the drain port .

Fig. 12. Conversion efficiency, gate dc current, and drain dc voltage versus input power for several RF load impedance values presented at the gate. V and . The green point (in online version) on the Smith . chart corresponds to the highest efficiency point at

C. Self-Synchronous Transistor Rectifier Results The measurements of the rectifier are performed in self-synchronous mode, i.e., there is no input RF power incident externally into the gate port of the PA, unlike in previous transistor rectifier work [20], [24]. The following parameters are varied in order, while keeping the other parameters constant and sweeping the input RF power at the drain port, and the results are described in the same order: 1) RF impedance at the gate, ; 2) load resistance at drain bias output, ; 3) gate dc bias, . The gate load–pull was performed to determine the optimum impedance for maximum efficiency with a constant resistive dc load of 98.5 (nominally 100 ) and a constant transistor gate bias in pinch-off of 4.4 V. The RF signal is coupled from the drain to the gate matching network through the feedback capacitance , and thus the precise impedance presented at the gate of the transistor is imperative to achieving high efficiency. Fig. 11 shows the time-domain voltage and current waveforms measured at the drain and gate RF port of the amplifier when the RF input power at the drain port is swept from 11 to 42 dBm. These values are chosen because the rectifier in PA operation gives up to 42-dBm output power. The feedback signal present at the gate allows for the rectifier to operate in self-synchronous mode without any additional control signal. Unlike in the synchronously driven case where an external generator is connected to the gate, here the impedance presented at the gate is always passive (inside the Smith chart), keeping the device in a safe operating mode. Measured RF–dc conversion efficiency is shown in Fig. 12 for four different RF gate impedances. A maximal conversion efficiency of 85% is achieved with a dc output voltage of 36 V and an input power at the drain of 42 dBm with . This peak efficiency is for a RF gate load of around 230 (green hexagon (in online version) in the Smith chart in Fig. 12), which

Fig. 13. Conversion efficiency and drain dc output voltage versus V and input power for several dc drain resistor values. . The highest efficiency of 85% is obtained at dBm with a V.

is the highest impedance that was achievable with the specific tuner in the setup. For the low gate impedance (red triangle (in online version) in the Smith chart), the efficiency is significantly lower. By observing the gate current [see Fig. 12(d)], it can be seen that, for a low RF gate impedance, the gate diode turns on at around dBm. Since the input power cannot be increased much beyond this point to avoid breakdown, this limits the dc voltage at the output to around 4 V. For the gate impedance with highest efficiency (green line (in online version) with hexagon symbol), the gate diode is off for input drain powers below 41 dBm, allowing for high dc voltage output. After the optimal gate impedance for highest efficiency was obtained, a power sweep for three different values in the drain output was obtained. From Fig. 13, a maximal efficiency of 85% was measured for a dc resistive load of 98 , while an efficiency drop of 13% was observed for a dc load of 21 with 40-dBm input power. As expected, the dc output voltage decreases from a maximum 30 V for at 40-dBm input

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Fig. 14. RF impedance at measured at the input (drain port) versus input V and power for several dc drain resistor values. .

Fig. 15. Measured conversion efficiency and drain dc voltage versus input and power for several dc gate voltage biases. For this data, .

power, to a maximum of 13.4 V for with the same input power. It is interesting to see how the input impedance of the rectifier at the RF drain port approaches 50 as the input power increases (Fig. 14). This is expected since the PA was designed for maximal saturated power delivered into a 50- load. This again points to the similarities between the same circuit operated as a power rectifier and a PA. Finally, the effect of the gate bias on the rectifier efficiency, output voltage, and input impedance was investigated. The gate impedance in this case was set for highest efficiency (230 ), and a dc load of 58 was selected in order to protect the transistor from high drain voltages that occur for the 98load that corresponds to the highest efficiency. The measurements were performed for six different values of gate bias , as shown in Fig. 15. With , a maximum efficiency of 83% was obtained with the transistor biased deeply into the pinch-off region with V, and a drop of only 3% was measured for V. Furthermore, the gate bias has a minimal impact on the output dc voltage or on the drain impedance. V. CONCLUSION In summary, this paper has addressed high-efficiency power rectifiers designed with harmonic terminations at the RF input

in analogy to high-efficiency PA design with harmonic terminations at the output. The applications of such power rectifiers include wireless power beaming [7], recycling power in highpower circuits [18], and ultra-fast switching integrated dc–dc converters with no magnetics [19]. The theory for an ideal rectification element is based on Fourier analysis and establishes the basic design parameters such as the relationship between output dc resistance and impedance at the fundamental frequency at the rectifier input that optimizes efficiency. The analysis also predicts the time-domain waveforms at the terminals of the rectification element and the efficiency as a function of on-resistance and dc output resistance. Specific results are derived for class-C and class-F classes of operation, as they are defined for PAs. These two cases are chosen for experimental validation with a 2.45-GHz diode and 2.14-GHz transistor rectifier, respectively. It is straightforward to repeat the derivation for other classes of operation, such as class-F, as shown in detail in [35]. The experimental results show that good agreement can be reached between theory and experiment with a Schottky-diode single-ended rectifier with finite class-C harmonic terminations, resulting in 72.8% efficiency for input power levels in the milliwatt range, intended for wireless power harvesting detailed in [15] and [29]. A GaN HEMT class-F power rectifier achieved 85% efficiency with 40-dBm input power across 98dc load with a dc output voltage V. The efficiency and output voltage of the self-synchronous rectifier are shown to depend on the input power at the drain, the impedance at the gate port and the dc load at the output drain bias line, but not on the gate bias. Time-domain large-signal measurements of a class-F PA configured as a rectifier show that one can accomplish the same rectifier efficiency as the amplifier drain efficiency in self-synchronous mode without external gate RF drive. This is somewhat surprising, and to the best of our knowledge, the first time this type of high-efficiency rectifier has been demonstrated. ACKNOWLEDGMENT The authors would like to thank Dr. D. Root and Dr. J.-P. Teyssier, both with Agilent Technologies, Santa Clara, CA, for the loan of the time-domain nonlinear measurement equipment and TriQuint Semiconductor, Richardson, TX, for the donation of the transistors. REFERENCES [1] T. C. Martin and N. Tesla, The Inventions, Researches and Writing of Nikola Tesla: With Special Reference to His Work in Polyphase Currents and High Potential Lighting. Milwaukee, WI: Lee Eng. Company, 1952. [2] E. Peterson and F. Llewellyn, “The operation of modulators from a physical viewpoint,” Proc. IRE, vol. 18, no. 1, pp. 38–48, Jan. 1930. [3] J. Nelson, “Some notes on grid circuit and diode rectification,” Proc. IRE, vol. 20, no. 6, pp. 989–1003, Jun. 1932. [4] C. Edwards, “Microwave converters,” Proc. IRE, vol. 35, no. 11, pp. 1181–1191, Nov. 1947. [5] R. George and E. Sabbagh, “An efficient means of converting microwave energy to dc using semiconductor diodes,” Proc. IEEE, vol. 51, no. 3, pp. 530–530, Mar. 1963. [6] W. Brown, “Experiments in the transportation of energy by microwave beam,” in IRE Int. Convention Rec., Mar. 1964, vol. 12, pp. 8–17.

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[7] W. Brown, J. Mims, and N. Heenan, “An experimental microwavepowered helicopter,” in IRE Int. Convention Rec., Mar. 1965, vol. 13, pp. 225–235. [8] O. E. Maynard, W. C. Brown, A. Edwards, J. T. Haley, G. Meltz, J. M. Howell, and A. Nathan, “Microwave power transmission studies. volume 1: Executive summary,” NASA, Tech. Rep. 19760008506, 1975. [9] D. Watson, K. Talbot, and C. Johnson, “A cyclotron-wave microwave power converter,” Proc. IEEE, vol. 53, no. 11, pp. 1797–1798, Nov. 1965. [10] D. Watson, R. Grow, and C. Johnson, “A cyclotron-wave rectifier for s-band and x-band,” IEEE Trans. Electron Devices, vol. 18, no. 1, pp. 3–11, Jan. 1971. [11] W. C. Brown, “High power, efficient, free-space microwave power transmission systems,” in 3rd Eur. Microw. Conf., Sep. 1973, vol. 2, pp. 1–4. [12] W. Brown, “The design of large scale terres trial rectennas for low-cost production and erection,” in IEEE-MTT-S Int. Microw. Symp. Dig., Jun. 1978, pp. 349–351. [13] W. Brown, “The history of power transmission by radio waves,” IEEE Trans. Microw. Theory Techn., vol. MTT-32, no. 9, pp. 1230–1242, Sep. 1984. [14] R. Gutmann and J. Borrego, “Power combining in an array of microwave power rectifiers,” IEEE Trans. Microw. Theory Techn., vol. MTT-27, no. 12, pp. 958–968, Dec. 1979. [15] E. Falkenstein, M. Roberg, and Z. Popovic, “Low-power wireless power delivery,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 7, pp. 2277–2286, Jul. 2012. [16] J. Hagerty, F. Helmbrecht, W. McCalpin, R. Zane, and Z. Popovic, “Recycling ambient microwave energy with broadband rectenna arrays,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 3, pp. 1014–1024, Mar. 2004. [17] E. Falkenstein, “Characterization and design of a low-power wireless power delivery system,” Ph.D. dissertation, Dept. Elect. Comput. Eng., Univ. Colorado at Boulder, Boulder, CO, 2011. [18] X. Zhang, L. Larson, P. Asbeck, and R. Langridge, “Analysis of power recycling techniques for rf and microwave outphasing power amplifiers,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 49, no. 5, pp. 312–320, May 2002. [19] S. Djukic, D. Maksimovic, and Z. Popović, “A planar 4.5-GHz DC–DC power converter,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 8, pp. 1457–1460, Aug. 1999. [20] M. N. Ruiz, R. Marante, and J. A. Garcia, “A class E synchronous rectifier based on an e-pHEMT device for wireless powering applications,” in IEEE MTT-S Int. Microw. Symp. Dig., Montréal, QC, Canada, 2012, pp. 1–3. [21] S. Imai, S. Tamaru, K. Fujimori, M. Sanagi, and S. Nogi, “Efficiency and harmonics generation in microwave to dc conversion circuits of half-wave and full-wave rectifier types,” in IEEE MTT-S Int. Microw. Symp. Dig., 2011, pp. 15–18, Workshop ser. Innovative Wireless Power Transmission: Technol., Syst., Appl.. [22] H. Takhedmit, B. Merabet, L. Cirio, B. Allard, F. Costa, C. Vollaire, and O. Picon, “A 2.45-GHz low cost and efficient rectenna,” in Proc. 4th Eur. Antennas Propag. Conf., Apr. 2010, pp. 1–5. [23] R. Marante, M. N. Ruiz, L. Rizo, L. Cabria, and J. A. Garcia, “A UHF class E2 DC/DC converter using gan hemts,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [24] M. Kazimierczuk and J. Jozwik, “Analysis and design of class E zerocurrent-switching rectifier,” IEEE Trans. Circuits Syst., vol. 37, no. 8, pp. 1000–1009, Aug. 1990. [25] F. Raab, “Class-E, Class-C, and Class-F power amplifiers based upon a finite number of harmonics,” IEEE Trans. Microw. Theory Techn., vol. 49, no. 8, pp. 1462–1468, Aug. 2001. [26] F. Raab, P. Asbeck, S. Cripps, P. Kenington, Z. Popovic, N. Pothecary, J. Sevic, and N. Sokal, “Power amplifiers and transmitters for RF and microwave,” IEEE Trans. Microw. Theory Techn., vol. 50, no. 3, pp. 814–826, Mar. 2002. [27] S. Kee, I. Aoki, A. Hajimiri, and D. Rutledge, “The class-E/F family of ZVS switching amplifiers,” EEE Trans. Microw. Theory Techn., vol. 51, no. 6, pp. 1677–1690, Jun. 2003. [28] M. Roberg and Z. Popović, “Analysis of high-efficiency power amplifiers with arbitrary output harmonic terminations,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 8, pp. 2037–2048, Aug. 2011.

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[29] M. Roberg, E. Falkenstein, and Z. Popović, “High-efficiency harmonically-terminated rectifier for wireless powering applications,” in IEEE MTT-S Int. Microw. Symp. Dig., Montréal, QC, Canada, 2012, pp. 1–3. [30] M. Roberg, J. Hoversten, and Z. Popović, “GaN HEMT PA with over 84% power added efficiency,” Electron. Lett., vol. 46, no. 23, pp. 1553–1554, Nov. 2010. [31] “Swap-x402 data sheet,” VTD, Brive, France, 2011. [Online]. Available: http://www.vtd-rf.com/pdf/productpresentation.pdf [32] J. Verspecht, “Calibration of a measurement system for high frequency nonlinear devices,” Ph.D. dissertation, Vrije Univ. Brussel (VUB), Brussels, Belgium, 1995. [33] G. Callet, J. Faraj, O. Jardel, C. Charbonniaud, J.-C. Jacquet, T. Reveyrand, E. Morvan, S. Piotrowicz, J.-P. Teyssier, and R. Quéré, “A new nonlinear hemt model for AlGaN/GaN switch applications,” Int. J. Microw. Wireless Technol. (Special Issue), vol. 2, no. 3–4, pp. 283–291, 2010. [34] J. Faraj, G. Callet, O. Jardel, A. El-Rafei, F. De Groote, R. Quéré, and J. Teyssier, “Time domain large signal characterization of self-biasing phenomena in switch-mode AlGaN/GaN hemts,” in 74th ARFTG Symp./IEEE MTT-S Int. Microw. Symp. Dig., Montréal, QC, Canada, 2012. [35] M. Roberg, “Analysis and design of non-linear amplifiers for efficient microwave transmitters,” Ph.D. dissertation, Univ. Colorado at Boulder, Boulder, CO, 2012.

Michael Roberg (S’09) received the B.S.E.E. degree from Bucknell University, Lewisburg, PA, in 2003, the M.S.E.E. degree from the University of Pennsylvania, Philadelphia, in 2006, and the Ph.D. degree from the University of Colorado at Boulder in 2012. From 2003 to 2009, he was an Engineer with Lockheed Martin–MS2, Moorestown, NJ, where he was involved with advanced phased-array radar systems. He is currently with the Defense Products and Foundry Services, TriQuint Semiconductor, Richardson, TX, where she is involved with wideband high-efficiency GaN MMIC PA design. His current research interests include high-efficiency microwave PA theory and design, microwave power rectifiers, monolithic microwave integrated circuit (MMIC) design, and high-efficiency radar and communication system transmitters.

Tibault Reveyrand (M’07) received the Ph.D. degree from the University of Limoges, Limoges, France, in 2002. From 2002 to 2004, he was a Post-Doctoral Scientist with CNES (French Space Agency). In 2005, he became a CNRS Engineer with the XLIM Laboratory, University of Limoges, Limoges, France. His research interests include the characterization and modeling of RF and microwave nonlinear components and devices. Dr. Reveyrand is a member of the IEEE MTT-11 “Microwave Measurements” Technical Committee. He was the recipient of the 2002 European GaAs Best Paper Award.

Ignacio Ramos (S’12) received the B.S. degree in electrical engineering from the University of Illinois at Chicago, in 2009, and is currently working toward the Ph.D. degree at the University of Colorado at Boulder. From 2009 to 2011, he was with the Power and Electronic Systems Department, Raytheon IDS, Sudbury, MA. His research interests include high-efficiency microwave PAs, microwave dc/dc converters, radar systems, and wireless power transmission.

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Erez Avigdor Falkenstein (S’07) was born in Haifa, Israel, in 1979. He received the “Handesaie” degree (associate degree) in electronics from the Amal Handesaim School Hadera, Hadera, Israel, in 1999, and the concurrent M.S./B.S. degrees in electrical engineering and Ph.D. degree from the University of Colorado at Boulder, in 2010 and 2012, respectively. From 1999 to 2003, he was with the Israel Defense Force, as part of a technological unit. From 2004 to 2012, he was with the University of Colorado at Boulder. Since 2007, he has been involved with research as part of the Active Antenna Group. He is currently with Qualcomm Inc., Boulder, CO. His research concerns far-field wireless powering for low-power densities. His research interests include antenna design and characterization, modeling and measurement of nonlinear devices at microwave frequencies, and power management.

Zoya Popović (S’86–M’90–SM’99–F’02) received the Dipl.Ing. degree from the University of Belgrade, Belgrade, Serbia, Yugoslavia, in 1985, and the Ph.D. degree from the California Institute of Technology, Pasadena, in 1990. Since 1990, she has been with the University of Colorado at Boulder, where she is currently a Distinguished Professor and holds the Hudson Moore Jr. Chair with the Department of Electrical, Computer and Energy Engineering. In 2001, she was a Visiting Professor with the Technical University of Munich, Munich, Germany. Since 1991, she has graduated 44 Ph.D. students. Her research interests include high-efficiency, low-noise, and broadband microwave and millimeter-wave circuits, quasi-optical millimeter-wave techniques, active antenna arrays, and wireless powering for batteryless sensors. Prof. Popović was the recipient of the 1993 and 2006 Microwave Prizes presented by the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) for the best journal papers and the 1996 URSI Issac Koga Gold Medal. In 1997, Eta Kappa Nu students chose her as a Professor of the Year. She was the recipient of a 2000 Humboldt Research Award for Senior U.S. Scientists of the German Alexander von Humboldt Stiftung. She was elected a Foreign Member of the Serbian Academy of Sciences and Arts in 2006. She was also the recipient of the 2001 Hewlett-Packard (HP)/American Society for Engineering Education (ASEE) Terman Medal for combined teaching and research excellence.

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Passive Subharmonic Generation Using Memoryless Nonlinear Circuits Zahra Safarian, Student Member, IEEE, and Hossein Hashemi, Senior Member, IEEE

Abstract—A passive subharmonic generation and frequency downconversion method using a memoryless nonlinear circuit coupled to a linear passive resonator is presented. The frequency downconverter can be used to transfer the energy from a high-frequency signal to a lower frequency without requiring any dc power supply. In the synchronous mode, the passive downconverter acts as a self-powered frequency divider. The characteristics of the self-powered frequency downconverter have been studied analytically, and design tradeoffs have been shown for the specific case of a cross-coupled differential pair nonlinearity. As an example, a low-frequency prototype is implemented with discrete components. Analytical results and design procedures are verified in discrete and integrated prototypes. Index Terms—CMOS, frequency conversion, frequency divider, nonlinear circuits, oscillators, subharmonic generation.

I. INTRODUCTION

P

ASSIVE frequency downconverters and subharmonic generators can transfer the energy from a high-frequency source to a lower frequency without dc power consumption. They can be particularly useful in low power and batteryless RF integrated systems. It is well known that when a signal is passing through a nonlinear and/or time-varying system, harmonics of the signal are generated at the output, irrespective of the input signal amplitude. However, in order to generate the subharmonic of the signal at the output, the input amplitude or power needs to be larger than a certain threshold. This is a known fact in frequency dividers such as injection-locked or regenerative frequency dividers. The main known technique for a passive frequency division is parametric frequency downconversion and division in which a subharmonic frequency is generated by exciting a nonlinear circuitry with memory or reactance (usually a varactor). These reactances transfer the energy from an ac source to the load and are capable of transferring power from one frequency to another. The downconversion using a reactive element was first observed and reported by North [1]. Later on in 1956, Manley and Rowe presented a general set of equations that relates the average powers at different

Manuscript received July 03, 2012; revised September 20, 2012; accepted September 21, 2012. Date of publication November 19, 2012; date of current version December 13, 2012. This work was supported in part by Corning Inc. and the National Science Foundation (NSF). This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with the Department of Electrical Engineering–Electrophysics, University of Southern California, Los Angeles, CA 90089-0271 USA (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222657

frequencies in an ideal nonlinear reactance, independent of the nonlinearity shape [2]. The operation principles and requirements of parametric subharmonic oscillation using the semiconductor varactors have been described in [3]. Since then, there have been several designs on parametric frequency dividers implemented on printed circuit board (PCB) using discrete components [4]–[11]. There have been a few recent publications that demonstrate integrated RF parametric frequency dividers and downconverters in a CMOS technology [12]–[14]. Subharmonic oscillations are also known in acoustic systems, where by applying a strong electric excitation greater than a certain threshold, subharmonics or fractional harmonics of the applied frequency are generated. As an example, such subharmonics have been observed and reported in quartz plates [15]–[18]. In this paper, a new method for passive subharmonic generation, utilizing a memoryless nonlinear core coupled to a linear passive resonator, is proposed in which the energy of a RF source transfers to a lower frequency without consuming dc power. This lower frequency can be synchronized to the frequency of the input source, enabling realization of a passive frequency divider. Section II illustrates the concept and the operation principle. Section III shows the derivation of the downconverter properties using nonlinear analysis, which is applied to an LC-tuned cross-coupled topology. Section IV demonstrates a few design examples. Specifically, a 130-nm CMOS integrated 12-GHz passive divide-by-2 is demonstrated [19]. Section V concludes this paper. II. FREQUENCY CONVERSION USING MEMORYLESS NONLINEAR CIRCUITS Memoryless nonlinear circuits combined with linear passives can be configured to generate frequencies that are different than the input frequency without the need for a dc power supply or consuming dc power. In other words, some or all of the energy of an input drive can be transferred to generating and sustaining new frequencies that may be synchronous or asynchronous with respect to the input frequency. Consider the circuit shown in Fig. 1(a). A dc supply voltage, , biases the transistors by supplying a dc current through them. With a large enough dc current, the small-signal conductance looking into the cross-coupled transistors becomes more . This negative than the LC resonator loss, i.e., causes an oscillation startup, and ultimately, a steady-state sinusoid at the frequency of the LC resonator is sustained due to the nonlinearity of active devices. Now, consider the circuit in Fig. 1(b) where the dc voltage supply is replaced with an ac sinusoidal voltage source at

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where is the saturation current of the identical BJTs and is the thermal voltage. The exponential of a cosinusoidal function can be expressed as [20] (3) where is the modified Bessel function of the first kind and order . Since modified Bessel functions of odd (even) order are odd (even) functions of their argument [20], the differential current across the active circuitry can be written as

Fig. 1. (a) Negative resistance oscillator. (b) Proposed passive subharmonic generator using memoryless nonlinear circuitry.

(4)

Fig. 2. Input/output voltage waveforms when MHz ); H, zoomed version is shown in the inset.

where and are the normalized common mode and differential voltages, respectively. In order to simplify the analysis, we consider the synchronous mode and assume that , where is an integer number. Therefore, can be derived as

MHz and , and

pF. A

frequency . We will show that, under the right conditions, this circuit can generate a steady-state sinusoidal output at frequency . In fact, we will show that there is no need for dc current through the transistors to generate this output (Section IV-C). Output frequency can be independent of the input frequency (asynchronous operation) or a subharmonic of the input frequency (synchronous operation). Fig. 2 shows a representative simulation of the circuit in the synchronous mode where . We hypothesize that the voltage waveform across a high quality factor resonator primarily contains frequency , the resonant frequency of the passive LC. Since the input signal at frequency is applied to a common mode of this circuit, we further hypothesize that the single-ended voltages across this circuit can be written as

(5) where only odd terms of and should be considered. Now, we can find the equivalent input admittance of the the active circuitry at frequency by taking the ratio of the differential current component at to the differential voltages as

(6) (1) where and are the differential and common mode voltage amplitudes, respectively, and is the phase angle between the two signals. The collector currents in the bipolar junction transistors (BJTs) can then be expressed as

(2)

where is assumed for simplicity. It is easy to see that since the modified Bessel functions are positive for positive arguments. Intuitively, this negative conductance enables starting and sustaining steady-state oscillation at . This intuitive reasoning will be concretely substantiated in Section III. III. ANALYSIS This section covers the analysis and simulation results of the passive frequency conversion scheme of Fig. 2.

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voltage. Therefore, at and thus,

,

,

(10)

Fig. 3. (a) Self-powered downconverter with state-variables. (b) Second-order model for the downconverter.

For , while the differential voltage is still small, we assume that the common mode voltage, , and common mode current, , remain approximately intact. With the approximate solution for , the differential equations in (8) simplify to (11)

A. Formulation and Analytical Approach Let us assume , , , and represent the single-ended output voltages and inductor currents, respectively [see Fig. 3(a)]. The input signal is also . Neglecting base currents in the BJTs, the following equations can be written:

(7) , Taking the independent state variables as , and , the set of differential equations for the system is

(8)

where given by

. Thus, where the dynamics of the circuit is governed by a second-order nonautonomous nonlinear differential equation. In this case, the circuit can be modeled as an RLC tank with the capacitor voltage and inductor current ( and ) as state variables and a nonlinear time-dependent current source that represents the differential current in the transistor pair [see Fig. 3(b)]. In order to derive the transient waveforms, quasi-harmonic approximation is used, where the transient and steady-state expressions for the voltage and current waveforms are assumed to resemble sinusoids with slowly time-varying amplitude and phase as [21]

(12) . The quasi-harmonic approximation is and valid as long as the RLC quality factor is reasonably large. By taking the derivatives of and in (12) with respect to time and replacing them in the original equation [see (11)], the following first-order differential equations for and are obtained:

is a time-varying nonlinear function vector

(13)

(9) where Thus, the dynamics of the circuit is described by a third-order nonautonomous nonlinear differential equation, where the differential voltage and current depend on the common-mode current . Some simplifying assumptions will be made in order to solve this equation, the validity of which will be verified with simulations, and ultimately, measurements. Assuming zero initial conditions for the inductor and capacitor, at , and are equal to the common mode input

(14) In order to convert the above nonautonomous differential equations to autonomous ones (i.e., remove explicit time dependency), the equations are averaged over one oscillation period,

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an integer. The following averaged autonomous nonlinear differential equations for the amplitude and phase can be found for different values of . 1) :

(16) 2)

Fig. 4. Transient behavior of the circuitry for: (a) V.

:

V and (b)

. Since the amplitude and the phase are slowly varying functions of time over the oscillation period, they are assumed to be constant in the averaging process. Therefore, the averaged differential equations for and are given by

(17) 3)

:

(15) In steady state, the amplitude and phase variations should be zero, i.e., and . Fig. 4(a) shows the numerical solution of (15) using MATLAB and the simulated transient voltage waveform using Spectre for the differential voltage when V. Fig. 4(b) shows the same graphs when V. Analysis and transient simulations consistently show growth and sustaining of a sinusoidal differential voltage for large input amplitudes, and zero differential output for small input voltages. Throughout this section, the BJT model used for calculations and simulations is PBR951 UHF wideband transistor with fA and . All the simulations and calculations are performed for H and pF, corresponding to a tuned frequency of approximately 2.64 MHz, and , corresponding to the inductor quality factor of 13 at 2.64 MHz.

(18) 4)

and

:

(19) By definition, the amplitude and phase variation should be zero in the steady state, i.e., and . Stability analysis of steady-state solutions offers the following startup condition for the batteryless driven nonlinear circuit of Fig. 3 (details in the Appendix):

B. Startup Condition—Synchronous Mode In this section, we find the minimum required input amplitude that causes growth of differential output voltage. To find a closed-form formula for the startup condition, the function in (15) is approximated with the first two terms of its Taylor-series expansion, i.e., . To simplify the analysis, we also assume that the input frequency is an integer multiple of output frequency, i.e., , where is

(20) Since

, requires the minimum to satisfy the startup condition. Furthermore, for the startup condition remains constant for all values of .

,

SAFARIAN AND HASHEMI: PASSIVE SUBHARMONIC GENERATION

Fig. 5. Minimum required input power for startup BJT saturation current .

Fig. 6. Minimum required input power for startup when .

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when

versus: (a) resonator quality factor

versus

, (b) resonator capacitance

, and (c)

Fig. 7. Normalized minimum required input power for startup versus resonator quality factor ( ).

Oftentimes, it is desirable to find the circuit startup condition and other properties in terms of input power instead of input voltage swing. In the synchronous mode, the average input power is (21) where is the largest period in the system. At startup and for small differential voltage, , the common-mode current is given by (10). In this case, the input power is simplified to (22) Equations (20) and (22) can be combined to find the minimum input power necessary to start a growing oscillation at . Fig. 5(a) shows the calculated and Spectre simulated minimum required input power for startup versus resonator quality factor for ; higher resonator relaxes the startup condition. Fig. 5(b) shows versus resonator capacitance, . For this simulation, the of the tank is kept constant at . Resonators with smaller requires lower for startup oscillation. This may be intuitively expected as, for the same , smaller capacitor corresponds to larger effective parallel resistance for the resonator. Fig. 5(c) shows versus BJT saturation current . For this simulation, only the parameter in the model file of the BJT transistor PBR951 has been changed. The minimum required input power reduces as increases corresponding to a steeper response and a smaller for the BJTs. Fig. 6 shows versus for . As predicted by the calculations, requires the minimum , and as increases,

stays almost constant. Finally, Fig. 7 shows the ratio of at to at versus . This ratio is approximately 2, suggesting that the minimum required input power to start a synchronous output at for is 3 dB more than that for , nearly independent of the quality factor. C. Steady-State Solutions—Synchronous Mode Nonzero steady-state amplitude and phase solutions in the synchronous mode, i.e., the integer, are found by setting and in (15). Fig. 8(a) and (b) shows the variation of the steady-state amplitudes as , and therefore, varies for and two different inductor values. As can be seen, by increasing increases smoothly (power/current limited region) and saturates at a specific value where it does not increase by increasing input power (voltage limited region). Since in deriving (15), we have assumed that has a relatively small amplitude, the calculation is not valid at large output swing values. As expected intuitively, oscillators with higher also requires smaller to achieve a certain output swing. Fig. 8(c) shows the variation of the steady-state amplitudes as varies for two different resonator capacitance , while and . With smaller , larger output swing for the same input power is achieved. The output power is defined as the power delivered to , the total parallel resistance of the tank (Fig. 1) (23)

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Fig. 8. Variation of the steady-state amplitudes

Fig. 9. Variation of the power efficiency

as

as

varies for

MHz when: (a)

varies for

MHz when: (a)

, (b)

, (b)

, and (c)

, and (c)

pF and

pF and

pF.

pF.

input voltage swing levels where is assumed to be an integer number. The circuitry shows the highest efficiency at . As increases, the efficiency does not change and it is almost half of the efficiency at . D. Effect of Detuning and Locking Range

Fig. 10. Variation of the power efficiency mV when .

versus

for

mV and

This resistor captures the resonator loss, represented by , as well as any explicit load resistance. In an ideal case, the resonator should be lossless and the load resistance, to which the power is intended for delivery, is the only contributor to . As such, all the references to the resonator quality factor are intended for the loaded quality factor. The power transfer efficiency can be derived as (24) for Fig. 9(a) and (b) shows power efficiency versus and two different inductor values. We can observe that, in the power/current limited region, power efficiency increases as increases. However, in the voltage-limited region, the efficiency drops by increasing , since the output voltage is almost constant. Higher also results in higher efficiency. Fig. 9(c) shows power efficiency versus for two different resonator capacitance . Lower capacitance results in higher power transfer efficiency. Fig. 10 shows power efficiency versus for different

In practice, the passive resonator frequency may not be exactly equal to an integer frequency of input frequency, i.e., . In this section, we derive the maximum frequency detuning for which the circuit still operates in the synchronous mode, i.e., it produces an output frequency that is exactly equal to , where is an integer number. Let us assume , where is an integer and represents the frequency detuning. For , the output waveform may have different behaviors. At small input voltage levels, as is detuned from integer values, the oscillation amplitude decreases until it dies [see Fig. 11(a)]. As the input amplitude increases, by detuning , the oscillation amplitude decreases until it goes out of the locking range where it has an asynchronous oscillation with amplitude much smaller compared to the integer [see Fig. 11(b)]. As input amplitude increases more, by detuning , the oscillation amplitude does not change, saturated at approximately the maximum value; however, as it goes out of the locking range, it has an asynchronous oscillation with negligible change in the peak amplitude [see Fig. 11(c)]. Now we want to find the detuning range or the locking range. If the output signal is synchronized with the input signal, its frequency will be equal to . For , we assume that (16)–(19) can still represent the average equations for the system. In this case, and represent the steady-state locking condition.

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Fig. 12. Phase portrait of the circuitry around the stable point at different values , (b) , (c) , and (d) for of : (a) and mV.

Fig. 11. Different scenarios for the oscillator output signal, when it is detuned : (a) , (b) , and (c) , where more than it can tolerate at different . Zoomed versions are shown in the respective insets.

For the other fixed point, we have of locking; thus, and the second fixed point is

at the edge . Therefore,

The detailed analysis is going to be shown for . In this case, there are two fixed points, . The first one is (28) (25) corresponding to oscillator dying down [see Fig. 11(a)]. To find the stability of this fixed point, the averaged equation is linearized around the fixed point. In this case, the eigenvalues of the linearized equation are

corresponding to asynchronous oscillations [see Fig. 11(b)]. Thus, the locking range equals

(29) (26) If is an integer number , will equal 0. As increases, and the input frequency is further detuned from , goes to the first or fourth quadrant [see (25)]. As an example, Fig. 12 shows the phase portrait of the circuitry around the stable point at different values of for and mV. Since in first and fourth quadrants, , consequently, . Thus, to find the locking range in this case, we only need to find the condition where stays negative. In this case, the locking range equals

(27) . Thus, in this case, by dewhen tuning more than derived in (27), the startup condition will not be satisfied and oscillation will be stopped.

derived in (29), the In this case, by detuning more than oscillator goes out of locking range and it shows asynchronous oscillation. As mentioned above, at the edge of these two regions, we have (30) Fig. 13 shows the input power at the edge of the oscillation dying and pulling versus . For this calculation, maximum is derived from (30) and then replaced in (22) to find . Fig. 14(a) shows the locking range versus the input power for and . The calculation uses (27) and (29) for each region. Since the model in not valid when the output voltage saturates, (29) cannot predict the locking range accurately in that case. Fig. 14(b) shows the locking range versus the input power for two different tank capacitance , while MHz and . Since lower capacitance requires lower power for oscillation, it provides higher locking range with smaller input power.

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Fig. 13. Input power at the edge of oscillation dying and pulling versus tank . quality factor

Fig. 15. Locking (tuning) range versus input power at .

and

for

Fig. 16. Simulated minimum required input power for startup versus: and (b) nMOS channel width at ; (c) the steady(a) , and (d) locking (tuning) range versus at and state amplitudes .

Fig. 14. Locking (tuning) range versus input power at and and (b) pF and pF.

Fig. 15 shows the locking range versus the input power for and when . For and , since , detuning does not have any effect on the oscillation frequency. Therefore, the circuit will show an asynchronous oscillation and the output signal cannot lock to the input signal (basically the locking range is zero).

for: (a)

E. MOSFET Nonlinear Core Following the same above-mentioned procedure, the locking range for in the two regions equals

(31)

, only oscillation pulling happens by detuning . The For reason is that for . Therefore, the locking range limited by the oscillation pulling is (32)

In Sections III-A–III-D, the nonlinear core is assumed to consist of BJT transistors. The exponential I–V characteristic of BJT eases the analysis and enables derivation of closed-form expressions from which intuition can be gained. In this section, we briefly discuss the effect of using MOSFET transistors in the nonlinear core. The I–V characteristic of MOS transistors is not as well behaved, especially as transistor enters different operation regions (e.g., saturation, triode) throughout the large-signal operation. However, based on the simulation results, the circuit function does not depend on the exact nonlinear function. The simulations are done for the same schematic shown in Fig. 3(a), except that the BJT transistors are replaced with nMOS transistors in a 0.13- m CMOS technology. The same passive devices have been used ( H, pF, , corresponding to a tuned frequency of approximately 2.64 MHz and of 13 at 2.64 MHz). Fig. 16(a) shows the minimum required

SAFARIAN AND HASHEMI: PASSIVE SUBHARMONIC GENERATION

Fig. 17. Measurement setup for the low-frequency prototype.

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Fig. 20. Measured output waveforms when the downconverter is pulled for at: (a) and (b) , where . Zoomed versions are shown in the respective insets.

Fig. 18. Measured single-ended and differential output waveforms when: and (b) . (a)

Fig. 21. (a) Detailed schematic and (b) chip microphotograph of the integrated 12-GHz divide-by-2 self-powered divider. Fig. 19. Measured, simulated, and calculated: (a) minimum required input for subharmonic generation versus the input frequency, power (b) locking (tuning) range, (c) output amplitude, and (d) power efficiency . versus input power at

input power for the startup versus with nMOS size of m nm. Similar to the case where BJT devices have been used, requires the minimum input power and as increases, is relatively constant and approximately 3 dB more than . Fig. 16(b) shows versus the width of the MOS transistor when channel length

is nm and . Again, we see that larger transistors and smaller threshold voltages are beneficial as they reduce the minimum input power requirement. also shows stronger dependence on the device size at small device sizes. Fig. 16(c) shows the steady-state amplitude versus , when m nm for in comparison with the BJT case.1 Fig. 16(d) shows the locking range versus the input power, which is very close in both the BJT and CMOS cases. 1The circuitry with this size of nMOS transistor requires the same fA. a circuitry using a BJT with

as

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Fig. 22. Measured and simulated: (a)

(return loss), (b) sensitivity curve, and (c) measured

versus the transistor bulk voltage.

IV. IMPLEMENTATION AND MEASUREMENT RESULTS In this section, measurements results for discrete and integrated prototypes verifying the analytical claims are presented. A. Discrete Frequency Downconverter To experimentally demonstrate the generation of various subharmonic signals in the synchronous operation mode and verify the corresponding locking ranges, the configuration shown in Fig. 2 is implemented. The BJTs and passives are the same used in calculations and simulations (the BJT transistor is PBR951, H, and pF). The measurement setup is depicted in Fig. 17. For the measurements, a high input-impedance oscilloscope (Tektronix TDS2024C) has been used; therefore, no output buffer was required. Since there is no matching circuitry at the input, directional couplers have also been used to extract the value of the input power that goes into the circuitry. Representative measured single-ended and differential output and waveforms of the circuit for are shown in Fig. 18(a) and (b), respectively. As expected, each single-ended signal has both the input frequency and output frequency components. Fig. 19(a) shows the measured, simulated, and calculated minimum required input for subharmonic generation (not necessarily power synchronous) versus the input frequency. As expected, dividing requires the minimum input power, and as by 2 frequency increases, almost a constant input power is required. As predicted before, the difference in for and is about 3 dB. The measured, simulated, and calculated locking range for versus the input power is depicted in Fig. 19(b). The differential output amplitude and power efficiency are shown in Fig. 19(c) and (d), respectively. A of 6 is assumed for the simulation and calculation to match to the measurement results. As an example, the measured differential output voltages during the circuit pulling at two different input are also shown in Fig. 20. power levels for B. Integrated 12-GHz Divide-by-2 Self-Powered Divider As shown before, division-by-2 requires lowest input power and also provides highest efficiency. In order to demonstrate the applicability of this technique at higher frequencies, an integrated 12-GHz divide-by-2 circuitry is designed and fabricated in a 0.13- m CMOS technology with eight metal layers (Fig. 21). As mentioned in Section IV-A, smaller threshold voltage for the switching pair transistors relaxes the startup

Fig. 23. Measured phase noise of the signal generator and the 12-GHz divider output.

condition; therefore, triple-well transistors have been used with positive bulk voltage to reduce the threshold voltage. The bulk and -well of the transistors have also been floated with a large resistance (1.1 M ) to reduce the parasitic capacitance. The ladder input at 12 GHz is matched to 50 using the network. From simulations, the loss of the matching circuitry network at 12 GHz is about 2 dB, while the of the resonance tank at 6 GHz is approximately 15. An open-drain output buffer has been placed after the divider to facilitate measurements. The -well and bulk voltages are kept at 1.5 and 0.5 V, respectively. Fig. 22(a) shows the small-signal input reflection cowhen dBm. The measured and simuefficient lated sensitivity curves (locking range) are shown in Fig. 22(b); the minimum required input power is about 2 dBm, while the dBm. locking range is approximately 1 GHz at Fig. 22(c) shows the measured versus the bulk voltage. As the bulk voltage increases, the threshold voltage of the nMOS transistors reduces; thus the input power for startup also reduces. Fig. 23 shows the measured phase noise of the signal generator (Agilent E8257C) and the 12-GHz divider output. Table I summarizes the performance of this 12-GHz divider in comparison with other recent reported passive and active dividers. C. Effect of a DC Block on the Divider Performance The simulated single-ended voltage and transistor current waveforms in the 12-GHz divider are shown in Fig. 24(a). The current waveform is asymmetric with respect to time so it has a dc component. This dc current helps the circuitry to satisfy the startup condition easier since smaller ac current (and therefore,

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TABLE I PERFORMANCE COMPARISON AMONG DIFFERENT PASSIVE AND ACTIVE DIVIDERS

Fig. 24. (a) Simulated single-ended voltage and transistor current waveforms. (b) Measured maximum/minimum generated dc current in the 12-GHz divider. (c) Measured sensitivity curve with/without dc block at the input.

smaller ) will be required for oscillation. The presence of the dc current in the system equations has also been shown in the previous sections . Fig. 24(b) shows the measured maximum and minimum generated dc current in the 12-GHz divider. However, the functionality of the frequency divider does not depend on the existence of the dc current in the circuit. To prove this, a dc block is placed in series with the input (the dc port of the bias-tee is floated now). Fig. 24(c) shows the measured sensitivity curve before and after using the dc block. The circuit functions with and without dc current. However, the performance of the circuit degrades significantly when the dc current is blocked. Strangely, in the case of low-frequency discrete prototype, the circuit does not function when the dc current is blocked. This is against our expectation and still not understood.

Fig. 25. Alternative configuration for the proposed passive subharmonic generator without any dc power supply and their representative inpu/output waveforms. (a) Differential cross-coupled oscillator with tail transistor MHz . (b) Differential noise-shifting Colpitts oscillator MHz [25].

V. CONCLUSIONS AND DISCUSSIONS This paper presents a passive frequency downconverter to transfer energy from a higher frequency source to a lower frequency, which can be a subharmonic of the input source, without consuming dc power. In the proposed technique, a memoryless nonlinear core coupled to a linear passive resonator is exploited for frequency downconversion. While all analysis, designs, and experimental results correspond to the cross-coupled differential pair active core, the principles are general and applicable to other similar circuits as well. Fig. 25 shows the proposed batteryless passive subharmonic frequency generation scheme with alternative nonlinear cores, along with their representative simulated input/output waveforms. The major motivation for this study is to enable batteryless systems that must extract energy from electromagnetic

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emissions. Extracting power from higher RF frequencies is advantageous from the antenna size standpoint. However, the main challenge with high-frequency power harvesting is the low RF-to-dc power conversion efficiency of most rectifiers. For example, a reported millimeter-wave power harvesting system shows the RF-to-dc conversion efficiency of around 1.2% for the rectifier at 45 GHz, including the losses of the on-chip matching network [26]. Efficient batteryless subharmonic generation followed with an efficient low-frequency rectifier may result in a more efficient solution for high-frequency power harvesting. APPENDIX A In this appendix, detailed analysis to find the startup condicase is presented. First, the fixed points or the tion for the solutions to the simplified averaged differential equations [see (16)] are found. In order to analyze the stability of these solutions, the eigenvalues of the Jacobean matrix [see (33)] should be evaluated at each fixed point

The second solution in (34) exists only when , in which case both of the following eigenvalues will be negative:

(36)

Consequently, this will be a stable steady-state solution when . The eigenvalues corresponding to the third solution in (34) are

(33) (37) The nonzero fixed points are which corresponds to a saddle point if and to an unstable point otherwise. Therefore, if , the second fixed point is the stable solution, satisfying the startup condition; otherwise, becomes the stable point. It should be mentioned that the above fixed points are valid for small values of amplitude, due to the approximation in the function, which is suitable for the startup condition.

(34)

The first solution, eigenvalues:

,

, has the following

(35) Therefore, , and is either a saddle point or an unstable point, depending on the value of . However, , will be a saddle point if (which provides the startup condition); otherwise, it is a stable point. This is when the startup condition is not satisfied.

REFERENCES [1] H. Q. North, “Properties of welded contact germanium rectifiers,” J. Appl. Phys., vol. 17, no. 11, pp. 912–923, Nov. 1946. [2] J. M. Manley and H. E. Rowe, “Some general properties of nonlinear elements—Part I: General energy relations,” Proc. IRE, vol. 44, no. 7, pp. 904–913, Jul. 1956. [3] J. Hilibrand, C. W. Mueller, C. F. Stocker, and R. D. Gold, “Semiconductor parametric diodes in microwave computers,” IRE Trans. Electron. Comput., vol. EC-8, no. 3, pp. 287–297, 1959. [4] R. G. Harrison, “A broadband frequency divider using microwave varactors,” IEEE Trans. Microw. Theory Techn., vol. MTT-25, no. 12, pp. 1055–1059, Dec. 1977. [5] Z. Nativ, “The application of a frequency multiplier design method to the design of microwave parametric dividers,” IEEE Trans. Microw. Theory Techn., vol. MTT-35, no. 2, pp. 189–194, Feb. l987. [6] G. A. Kalivas and R. G. Harrison, “A new slotline-microstrip frequency halver,” in IEEE MTT-S Int. Microw. Symp. Dig., 1985, pp. 683–686. [7] R. G. Harrison and W. D. Cornish, “Varactor frequency halver with enhanced bandwidth and dynamic range,” in IEEE MTT-S Int. Microw. Symp. Dig., 1986, pp. 305–308. [8] S. P. Stapleton and M. G. Stubbs, “A microwave frequency halver with conversion gain,” in Eur. Microw. Conf. Dig., 1986, pp. 749–753. [9] G. R. Sloan, “The modeling, analysis, and design of filter-based parametric frequency dividers,” IEEE Trans. Microw. Theory Techn., vol. 41, no. 2, pp. 224–228, Feb. 1993. [10] A. Suárez and R. Melville, “Simulation-assisted design and analysis of varactor-based frequency multipliers and dividers,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 3, pp. 1166–1179, Mar. 2006.

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[11] Z. Heshmati, I. C. Hunter, and R. D. Pollard, “Microwave parametric frequency dividers with conversion gain,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 10, pp. 2059–2064, Oct. 2007. [12] Z. Zhao, J. Bousquet, and S. Magierowski, “Coherent parametric RF downconversion in CMOS,” in IEEE MTT-S Int. Microw. Symp. Dig., 2010, pp. 377–380. [13] S. Magierowski, J. Bousquet, Z. Zhao, and T. Zourntos, “RF CMOS parametric downconverters,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 3, pp. 518–528, Mar. 2010. [14] W. Lee and E. Afshari, “Distributed parametric resonator: A passive CMOS frequency divider,” IEEE J. Solid-State Circuits, vol. 45, no. 9, pp. 1834–1844, Sep. 2010. [15] M. Luukkala, “Fine structure of fractional harmonic phonons,” Phys. Lett. A, vol. 25, no. 2, pp. 76–77, Jul. 1967. [16] M. Luukkala, “Threshold and oscillation of fractional phonons,” Phys. Lett. A, vol. 25, no. 3, pp. 197–198, Aug. 1967. [17] H. Mahon, E. Brun, M. Luukkala, and W. G. Proctor, “Excitation of fractional harmonic phonons in solids,” Phys. Rev. Lett., vol. 19, no. 8, pp. 430–432, 1967. [18] P. J. King and M. Luukkala, “Subharmonic generation in quartz plates,” J. Phys. D, Appl. Phys., vol. 6, pp. 1047–1051, 1973. [19] Z. Safarian and H. Hashemi, “Passive subharmonic generation using LC-oscillators,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [20] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, 9th ed. New York: Dover, 1972, pp. 358–364. [21] N. Kryloff and N. Bogoliuboff, Introduction to Nonlinear Mechanics. Princeton, NJ: Princeton Univ. Press, 1947. [22] R. Sujiang, A. W. L. Ng, and H. C. Luong, “0.9 mW 7 GHz and 1.6 mW 60 GHz frequency dividers with locking-range enhancement in 0.13 m CMOS,” in Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2009, pp. 96–97. [23] Y. Chen, M. Li, H. Kuo, T. Huang, and H. Chuang, “Low-voltage -band divide-by-3 injection-locked frequency divider with floatingsource differential injector,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 1, pp. 60–67, Jan. 2012. [24] Z. Huang, C. Wu, and B. Huang, “Design of 24-GHz 0.8-V 1.51-mW coupling current-mode injection-locked frequency divider with wide locking range,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 8, pp. 1948–1958, Aug. 2009. [25] R. Aparicio and A. Hajimiri, “A noise-shifting differential Colpitts VCO,” IEEE J. Solid-State Circuits, vol. 37, no. 12, pp. 1728–1736, Dec. 2002. [26] S. Pellerano, J. Alvarado, and Y. Palaskas, “A mm-wave power-harvesting RFID tag in 90 nm CMOS,” IEEE J. Solid-State Circuits, vol. 45, no. 8, pp. 1627–1637, Aug. 2010.

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Zahra Safarian (S’12) received the B.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 2005, the M.S. degree in electrical engineering from the University of Southern California (USC), Los Angeles, in 2008, and is currently working toward the Ph.D. degree at USC. The focus of her current research is the design of low-power integrated systems for biomedical applications.

Hossein Hashemi (S’99–M’03–SM’08) received the B.S. and M.S. degrees in electronics engineering from the Sharif University of Technology, Tehran, Iran, in 1997 and 1999, respectively, and the M.S. and Ph.D. degrees in electrical engineering from the California Institute of Technology, Pasadena, in 2001 and 2003, respectively. In 2003, he joined the Ming Hsieh Department of Electrical Engineering Electrophysics, University of Southern California (USC), Los Angeles, where he is currently an Associate Professor, Ming Hsieh Faculty Fellow, and Co-Director of the Ming Hsieh Institute. His research interest spans mathematics, physics, and realization of integrated electrical and optical systems. Dr. Hashemi currently serves on the Technical Program Committees of the IEEE International Solid-State Circuits Conference (ISSCC), the IEEE Radio Frequency Integrated Circuits (RFIC) Symposium, and the Compound Semiconductor Integrated Circuits Symposium (CSICS). He was an associate editor for the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—PART I: REGULAR PAPERS (2006–2007) and the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—PART II: EXPRESS BRIEFS (2004–2005). He was the recipient of the 2008 Defense Advanced Research Projects Agency (DARPA) Young Faculty Award, the National Science Foundation (NSF) CAREER Award, and the USC Viterbi School of Engineering Junior Faculty Research Award (2008). He was recognized as a Distinguished Scholar for the Outstanding Achievement in Advancement of Engineering by the Association of Professors and Scholars of Iranian Heritage (2011). He was a corecipient of the 2004 IEEE JOURNAL OF SOLID-STATE CIRCUITS Best Paper Award and the 2007 IEEE International Solid-State Circuits Conference (ISSCC) Lewis Winner Award for Outstanding Paper.

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Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique Han-Chih Yeh, Student Member, IEEE, Chau-Ching Chiong, Student Member, IEEE, Sofiane Aloui, and Huei Wang, Fellow, IEEE

Abstract—In this paper, the design and analysis of CMOS low-noise amplifiers (LNAs) with a magnetic coupled technique in different cascode topologies are proposed. To minimize the noise figure (NF) and the supply voltage, and to guarantee large 3-dB bandwidth, transformers are designed and placed between the transistors of the cascode devices. Three low supply voltage and wideband LNAs are designed, fabricated, and tested for demonstration. The first LNA uses the magnetic coupled cascode configuration. The second LNA is consisted of magnetic coupled cascode configuration with two amplification stages. The third one-stage LNA is based on the magnetic coupled triple cascode configuration. The first LNA is designed at -band while the others are designed at -band, using 90-nm low-power CMOS technology. The -band LNA has a gain of 13.8 dB and an NF of 3.8 dB at 37 GHz, with a power consumption of 18 mW at 1.2-V supply voltage. The -band cascode LNA has a gain of 17 dB at 57 GHz and an NF of 4.4 dB at 59.5 GHz with a power consumption of 19.2 mW at 1.2-V supply voltage. The -band triple-cascode LNA has a gain of 13.7 dB at 54 GHz and an NF of 5.3 dB at 59.5 GHz, with a power consumption of 14.4 mW at 1.2-V supply voltage. Compared with the conventional cascode LNAs, the proposed magnetic coupled cascode LNAs have better NF, larger gain bandwidth product, and lower power consumption. The use of the magnetic coupled technique in a multicascode LNA significantly improves the gain performance with a slight degradation of the NF. Index Terms—Cascode, CMOS, low-noise amplifier (LNA), monolithic microwave integrated circuit (MMIC).

I. INTRODUCTION

F

OR LOW-NOISE amplifier (LNA) implementation, common-source (CS) configuration with inductive source degeneration and transformer feedback technique are usually

Manuscript received July 10, 2012; revised September 20, 2012; accepted September 24, 2012. Date of publication November 21, 2012; date of current version December 13, 2012. This work was supported in part by the National Science Council (NSC) under NSC Grant 98-2219-E002-005 and NSC Grant 98-2219-E002-010 and by National Taiwan University under Excellent Research Project 95R0062-AE00-01. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. H.-C. Yeh and H. Wang are with the Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei 10617, Taiwan (e-mail: [email protected]). S. Aloui was with the Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei 10617, Taiwan. He is now with the Electrical Engineering School, Ecole Nationale Superieure de l’Electronique et de ses Applications (ENSEA), CergyPontoise 95000, France C.-C. Chiong is with the Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), Taipei 10617, Taiwan. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2224365

adopted [1]–[5] to satisfy low supply voltage requirements. When the operation frequency increases, CS configuration suffers from low-power (LP) gain. Thus, the multicascade stage is required. This results in a large chip size. To overcome this, in recent years, a cascode or a multicascode topology is adopted for millimeter-wave (MMW) LNA design [6]. However, cascode or multicascode topology has some disadvantages. The common-gate (CG) transistors contribute considerable noise at the output port. A high supply voltage is also needed. In order to reduce the noise contributed by CG transistors in cascode or multicascode topology, the series resonant inductors [6] or the parallel resonant inductors [7] are designed and placed between the CG devices. However, these solutions enlarge the chip areas. Therefore, the transformer is designed and placed between the multicascode devices to form the equivalent inductors [8]. This technique has the same concept as the inter-stage inductors technique used in [6]. It makes a compromise between the noise figure (NF) and the chip size. All reported techniques can reduce the NF, but they still require a high supply voltage in the multicascode topology. In order to reduce the NF and the supply voltage of the cascode or multicascode configuration simultaneously, a magnetic coupled technique is proposed in our previous study [9]. In this technique, the coupling effect of the transformer is used to couple the RF input signal between CG devices of the cascode or multicascode structures, which is different from [8] and [6]. In this paper, the analysis and design of the magnetic coupled technique used in the cascode and the multicascode configurations are presented. The transformers minimize the effect of the parasitic capacitances of the cascode or the multicascode device in the desired band. Furthermore, the dc path of the cascode or multicascode configuration is separated using these transformers. Thus, the NF and the supply voltage of the cascode or multicascode configuration are simultaneously minimized. Besides the LNA reported in [9], the other two -band LNAs using the magnetic coupled cascode and triple-cascode topologies are also designed for demonstration. Based on this approach, the -band LNA [9] employs a one-stage magnetic coupled cascode and a CS buffer stage to achieve a gain of 13.8 dB and an NF of 3.8 dB at 37 GHz. The -band magnetic coupled cascode LNA has a measured gain of 17 dB at 57 GHz and an NF of 4.4 dB at 59.5 GHz. Besides, the -band magnetic coupled triple-cascode LNA presents a measured gain of 13.7 dB at 54 GHz an NF of 5.3 dB at 59.5 GHz. It is important to underline that the - and -band cascode LNAs are all designed with a 1.2-V supply voltage.

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Fig. 1. Schematic of a cascode device with a: (a) parallel and (b) series resonant inductor.

Fig. 3. Schematics of the: (a) cascode and (b) cascode device with the magnetic coupled transformer. Fig. 2. (a) Transformer and (b) simplified equivalent model of the transformer.

II. CASCODE DEVICE WITH MAGNETIC COUPLED TECHNIQUE A. Analysis of the Proposed Topology and The cascode device consists of a CS nMOS transistor a CG nMOS transistor . At MMW frequencies, the NF of the cascode device will increase significantly due to the parasitic capacitances between and [6], and thus, it should be resonated out. Fig. 1 shows a cascode device with a parallel [7] or a series [6] resonant inductor. is the total parasitic capacitance between the node of a cascode device, as shown in Fig. 1. and are the inductors used to resonate the parasitic capacitances out. These two techniques are effective for reducing the NF of the cascode device at MMW frequencies. If these two noise-reduction techniques are combined and applied to the cascode device, the NF of the cascode device will be further reduced. However, performing this combination will occupy a large area. Fig. 2 shows the simplified equivalent model of a transformer. The simplified model of the transformer, as shown in Fig. 2(b), can be considered as a combination between series and parallel inductors. Therefore, a compact transformer can be inserted into the node between and for noise and area reduction. Fig. 3 illustrates the schematics of the cascode and cascode device with the magnetic coupled transformer. The transformer is composed of the inductors and with the mutual magnetic coupling coefficient [cf. Fig. 3(b)]. It is placed between the CS transistor and the CG transistor of the cascode device to not only reduce the noise contributed by , but also to keep a low supply voltage, as used in a CS device. To illustrate, the supply voltage of the cascode device is (2.4 V for GP device and 2 V for a low-power (LP) device using 90-nm CMOS technology). However, for system considerations, the supply voltage is usually limited to (1 or 1.2 V). Applying 1 V in a conventional cascode device will degrade the RF performances because will operate in the triode region. Since the transformer separates the dc path of and , the supply voltage can be half of the conventional cascode device. There-

Fig. 4. Schematic of the cascode device with a noise-reduction transformer using the transformer equivalent model, as shown in Fig. 2(b).

fore, the cascode device can be applied to implement LNAs for low-voltage applications. Note that the power consumption of the conventional cascode topology can be reduced by using the current-reuse technique. However, in the proposed topology, the dc biasing of the CS and CG stages are decoupled, and therefore, each transistor needs its own separate dc current, which can increase the required dc current consumption. The device sizing is according to the method developed in [10]. and have a total gate width of 28 and 42 m, respectively. The transistor size of is selected to ensure enough of this LNA. In the following analysis, drain-to-source resistance, the parasitic effects of and , and the channel length modulation effects are neglected. Fig. 4 illustrates the schematic of the cascode device including the simplified equivalent model of the added transformer. The noise contributed by at the output port can be expressed as (1) is the impedance looking into node where pressed as

. It can be ex-

(2)

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It is observed that if in the denominator of (1) tends to infinity, (1) tends to 0. Thus, the output noise in (1) can be minimized. This means that the denominator of (2) should tend to 0. Accordingly, (3) From (3), the design equation for the noise-reduction transformer can be derived as

(4) where (5) and is the resonating angular frequency for noise reduction in the desired band. Since the device size of the cascode cell and the angular frequency, which the noise-reduction technique will be applied, are determined, , , and can be treated as constant. Moreover, in order to compromise between area and frequency response in our design, is selected as 0.7 [11]. Therefore, the design parameters of (4) are only and . According to (4) and with a careful selection of inductor and , the effects of parasitic capacitances are minimized in-band so that the of the cascode cell is minimized. Note that in (4), the noise contribution of can be minimized by proper choice of transformer parameters. This can be verified by the simulated results that the smaller , , and , the smaller noise contribution of will be. The analysis of the cascode device with the noise-reduction transformer is applied in a -band LNA. Fig. 5 illustrates the simulated MSG/MAG and of the cascode device with the noise-reduction transformer. From Fig. 5(a), it is observed that with nH and nH, the cascode device has a stability factor higher than unity for the frequencies above 70 GHz. The transformer makes the turning point of the MSG/MAG curve approach to the desired band (50 70 GHz). Also, from Fig. 5(b), is reduced from 5.3 to 3.9 dB at 70 GHz. The NF of the cascode configuration can be minimized with the transformer parameters combination, which is selected based on (3). However, the proposed topology is unstable in the desired band. Considering the tradeoff between the stability and the NF of the proposed topology, the transformer parameters combination is selected as nH and nH with . Note that the transformer does not change optimum source impedance much. The optimum source impedance of the proposed topology is almost the same with the optimum source impedance of the conventional cascode configuration. The simulated of the cascode configuration without the transformer is 4.3 dB, whereas the cascode with the transformer is 3.3 dB at 60 GHz. Therefore, the reduction of the NF can be achieved in the proposed topology. In order to illustrate the advantages of the proposed topology quantitatively, the MSG/MAG and of the different topologies (the proposed topology, conventional cascode, cas-

Fig. 5. Simulated: (a) MSG/MAG and (b) various inductances.

of the cascode device with

code with parallel inductor, and cascode with series inductor) are compared and discussed here. For a -band single-stage LNA design, the turning point of the MSG/MAG versus frequency curve can be selected around the target frequency to avoid instability. Thus, when a series inductor or a noise-reduction transformer is applied to the cascode cell, and can be selected with the total gate width of 28 and 42 m, respectively. However, under this condition, the device size of and in a conventional cascode LNA will be set to 60 and 90 m, respectively. With a parallel inductor , the device size of and is the same as the case of the conventional cascode LNA. Fig. 6 illustrates the simulated MSG/MAG and of the cascode device, the cascode device with a series inductor, the cascode device with a parallel inductor, and the cascode device with a noise-reduction transformer under the condition of the same power consumption. From Fig. 6(a), it is observed that the cascode device with the noise-reduction transformer improves MSG/MAG

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Fig. 7. (a) Cascode cell with the equivalent model of the noise-reduction transformer. (b) Equivalent small-signal model of the cascode cell with the noise-reduction transformer.

Fig. 6. Simulated: (a) MSG/MAG and (b) versus frequency of the con:0.12 nH, cascode with :0.07 nH, and ventional cascode, cascode with cascode with the noise-reduction transformer.

According to Fig. 6, the cascode device with the transformer improves the gain and the NF in the desired band. Moreover, one of the main advantages of the proposed cascode topology is to improve linearity, especially as the voltage supply scales down with the technology. At 60 GHz, the simulated of the proposed topology ( : 28 m, :42 m, nH and nH with , conventional cascode configuration ( : 28 m and : 42 m), and CS configuration ( : 28 m) is 5, 5.5, and 4.5 dBm, respectively. The simulated results are obtained under the condition of the same power consumption. From the simulated results, the proposed topology exhibits comparable linearity with the CS configuration. In the following, the input impedance of the proposed topology is presented. Since the load impedance of is changed by the noise-reduction transformer, the input impedance of Fig. 7(a) is also influenced. Fig. 7(b) illustrates the equivalent small-signal circuit model of the cascode cell with the noise-reduction transformer, as shown in Fig. 7(a). The noise-reduction transformer, , can be derived as (6)

compared with the other three cases. From Fig. 6(b), it is observed that the cascode device with the noise-reduction transformer, the cascode device with the series inductor, and the cascode device with the parallel inductor have of 3.9, 4.2, and 5.3 dB at 70 GHz, respectively. The cascode device with the noise-reduction transformer has the lowest among the discussed noise-reduction techniques. Note that the NF of a cascode device can be reduced by using these three techniques. Nevertheless, the high supply voltage (2 or 2.4 V) is required, except for the case using the noise-reduction transformer. The high supply voltage characteristic is undesired for system integrations.

and (7), shown at the bottom of this page. The instability condition of the proposed topology can be derived from (6). Thus, the impact of the transformer on stability can be predicted. The trend is shown in Fig. 8, which illustrates the simulated input impedances of the cell with the noise-reduction transformer consisting of and with . It is observed that when and both increase, the proposed topology will be more unstable. The cascode device with the noise-reduction transformer has instability issue when is greater than 0.3 nH, and is greater than 0.3 nH with equal to 0.7. will have

(7)

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Fig. 8. Simulated input impedances of the cascode cell with the noise-reduction and with . transformer consisting of various

a negative real part for frequencies around 50 GHz. Nevertheless, when is 0.7 nH and is 0.7 nH with , the proposed topology becomes stable at the frequencies above 53 GHz. Therefore, the input matching of the cascode cell with the noise-reduction transformer needs to be carefully designed to satisfy the unconditional stable condition. Note that the transformer parameters do not have a significant influence on the reverse isolation of the proposed topology. The cascode configuration has better reverse isolation than the CS configuration due to the CG stage in the cascode cell. This can be verified by the simulated results. With various transformer parameters, the simulated reverse isolations of the proposed topology are all below 26 dB in the desired band (50 70 GHz). B. Analysis of Magnetic Coupled Transformer Multicascode Topology The multicascode LNA has advantages of high gain performance and compact chip size. However, the need of high supply voltage is still an issue for system integration. In order to illustrate the design concept of multicascode configuration with the noise-reduction transformers, a triple-cascode configuration is discussed first. Fig. 9(a) illustrates the schematic of the conventional multicascode configuration, which consists of a CS transistor and the CG transistors . Fig. 9(b) also depicts the schematic of the multicascode device with the noise-reduction transformers. For a triple-cascode configuration , the device sizes of , , and are set to 24, 48, and 72 m, respectively, according to the mentioned reasons discussed in Section II-A. At high frequencies, the parasitic capacitances of and contribute noise at the output port. To overcome

Fig. 9. (a) Schematics of the conventional multicascode configuration. (b) Multicascode device with the noise-reduction transformers.

this, two transformers, and with , , and with , are designed and placed between the triplecascode device. By adding the transformers to the triple-cascode cell , the input impedances looking from node and can be written as

(8)

(9) In order to cancel the noise contribution caused by , and should be as high as possible (ideal case: and ). Therefore, the denominators of (8) and (9) should tend to 0. Consequently, are calculated from the following equations:

(10)

(11)

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Fig. 11. Schematics of the triple-cascode device in comparison with: (a) parallel, (b) series noise-reduction inductors, and (c) noise-reduction transformers.

TABLE I DEVICE SIZES AND SIMULATED RESULTS OF DIFFERENT TOPOLOGIES, AS SHOWN IN FIG. 11

Fig. 10. Simulated: (a) MSG/MAG and (b) with various inductances.

of the triple-cascode device

where (12) By using (10) and (11), the effect of the parasitic capacitances can be minimized. Thus, the NF and the supply voltage of the triple-cascode configuration can be reduced. Fig. 10 illustrates the simulated MSG/MAG and of the triple-cascode device versus the frequency with various combinations of , , , and with . It is observed that when the inductances , , , and are larger, the triple-cascode configuration will be more stable. Moreover, when nH, nH, nH, and nH, the triple-cascode cell is stable above 70 GHz and without any degradation of the MSG at frequencies below 70 GHz. At the same time, is improved from 7.7 to 4.6 dB at 70 GHz. Thus, the triple-cascode configuration can be applied to implement a -band LNA. Fig. 11 illustrates the schematics of the triple-cascode device with the different noise-reduction techniques. In order to provide the quantitative descriptions about the advantages of the

triple-cascode device with the magnetic coupled transformers (similar to Section II-A), the simulated MSG/MAG and of the different topologies (cf. Fig. 11) are briefly described here. In the same fashion as described in Section II-A, these three different topologies are compared under the condition of the same power consumption. The turning point of MSG/MAG versus frequency curve is set to 69 GHz for these three cases since the desired band is -band. The simulated results are listed in Table I. From the simulated results, the triple cascode with the noise-reduction transformers improves MSG/MAG compared with the other two cases. Moreover, the triple cascode device with the noise-reduction transformers has the best compared with the other configurations at frequencies above 35 GHz. Hence, this configuration can be used to implement a -band CMOS LNA. In a multicascode LNA, high supply voltage is a major concern for system applications. The supply voltage of the multicascode configuration using the noise-reduction transformers is significantly reduced. The reason is that the transformers separate the dc paths of , as shown in Fig. 11(b), where represents the number of cascode stages. Moreover, the design equations of the multicascode device with the transformers can be derived by using the similar concept mentioned in Section II-A. Thus, the transformers that are between the CG transistors can be designed according to (13) and (14), shown at the bottom of the following page. Consequently, the transformers consisted of and

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Fig. 12. Simulated MSG/MAG and of the quadruple-cascode and quadruple cascode with noise-reduction transformers ( :0.3 nH, :0.2 nH, :0.3 nH, :0.18 nH, :0.3 nH, and :0.12 nH, ).

is designed for noise and supply voltage reduction in a multicascode LNA. For instance, (quadruple-cascode case), simulated MSG/MAG and with and without noise-reduction transformers are shown in Fig. 12. It is observed that for , the quadruple-cascode has a high MSG of 27.2 dB at 60 GHz with an of 7.6 dB. With the noise-reduction transformers, the turning point of MSG/MAG versus frequency curve moves from 95 to 75 GHz. At the same time, is improved from 7.6 to 3.5 dB at 60 GHz. Thus, the quadruple-cascode device can be applied to implement a high-gain -band LNA. Moreover, the supply voltage of quadruple-cascode device can also be reduced from 4 (4 or 4.8 V) to 1 (1 or 1.2 V). III. LNA IMPLEMENTATION Three LP and wideband LNAs are fabricated using a 90-nm LP CMOS process for demonstration. Two are cascode and triple-cascode LNAs, which are designed at -band; the other is a one-stage cascode LNA with a CS buffer stage, which is designed at -band [9]. A.

-Band LNA With Cascode Device

The -band LNA is implemented in TSMC commercial 90-nm LP CMOS technology [9], which provides

Fig. 13. Simulated: (a) MSG/MAG and (b) of the magnetic coupled and various combinations of . cascode configuration with

one-poly-nine-metal (1P9M). A top ultra-thick metal of a 3.3- m, metal–insulator–metal (MIM) capacitor and a polysilicon resistor are also available. The and of the 90-nm LP CMOS process are 130 and 110 GHz, respectively [12]. As previously discussed in Section II-A, the transformer consisting of and should be carefully designed to reduce the NF, instability,, and supply voltage of the cascode cell according to (4) and (5). Fig. 13 illustrates the MSG/MAG and

(13) (14)

YEH et al.: ANALYSIS AND DESIGN OF MMW LOW-VOLTAGE CMOS CASCODE LNA

Fig. 14. Circuit schematic of the proposed

Fig. 15. Chip photograph of the including all testing pads.

-band LNA.

-band LNA with a size of 0.93

0.52 mm

of the magnetic coupled cascode configuration versus the operation frequency with various combinations of and with [11]. The size of the transistor is a 16-finger nMOS with a total gate width of 40 m and is a 24-finger nMOS with a total gate width of 60 m. From Fig. 13, it is observed that the larger inductances and enhance the stability of the cascode cell, whereas can be also reduced for the frequency higher than 10 GHz. Moreover, it is also observed that with nH, nH, , the magnetic coupled cascode configuration is stable above 50 GHz; in the meanwhile, is improved from 2.9 to 2.4 dB at 40 GHz. Again, in the same fashion as described in Sections II-A and II-B, the cascode device with a series inductor, the cascode device with a parallel inductor, and the cascode device with the noise-reduction transformer are compared. From the simulated results, the cascode device with noise-reduction transformers has a MAG of 13.8 dB and of 3 dB at 50 GHz. Besides, the cascode with parallel inductors has an MSG of 10.8 dB and of 3.1 dB, whereas the cascode with series inductors has an MSG of 13.7 dB and of 5.8 dB at 50 GHz. In conclusion, the cascode device with a noise-reduction transformer improves MSG/MAG and compared with the rest of the cases at -band.

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Fig. 16. Circuit schematic of the topology.

-band LNA with magnetic coupled cascode

Fig. 17. Chip photograph of the including all testing pads.

-band LNA with a size of 1.0

0.59 mm

Fig. 14 illustrates the complete circuit schematic of the proposed -band LNA with a single-stage magnetic coupled cascode topology and a CS buffer stage. The buffer stage is designed for measurement considerations. A shunt inductor and a series inductor are utilized to implement the input matching network. , , , , and are utilized to implement the inter-stage matching network. Besides, a shunt inductor and a series inductor are utilized to implement the output matching network. Small inductors are utilized to implement all the matching networks, except and . Since the inductances of and are too large, the transformer with is utilized for implementation for saving the die area. The gate voltage is provided through a 10-k poly resistor, and the drain supply is via the bypass circuit. A chip photograph is presented in Fig. 15 with a chip size of 0.93 0.52 mm including all the testing pads. B.

-Band LNAs With Cascode and Triple Cascode Device

The -band LNAs are also implemented in a TSMC LP 90-nm CMOS process. Fig. 16 illustrates the circuit schematic of the -band magnetic coupled cascode LNA. The device size of and are selected to be 24 and 36 m. Two amplification stages with the noise-reduction transformers consisting of nH and nH with [11] are

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Fig. 18. Circuit schematic of the LNA.

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-band magnetic coupled triple-cascode

Fig. 20. Simulated and measured: (a) small-signal gains and return losses and (b) reverse isolation and simulated stability factor of the -band LNA.

Fig. 19. Chip photograph of the -band magnetic coupled triple-cascode LNA with a size of 0.6 0.48 mm including all testing pads.

adopted to achieve the high gain, low noise, and broadband performances. These noise-reduction transformers are designed according to (4) and (5), as mentioned in Section II-A. A shunt inductor and two series inductors and are utilized to implement the input matching network. , , , , and are utilized to implement the inter-stage matching network. A shunt inductor and a series inductor , are also utilized to implement the output matching network. A chip photograph of the -band LNA is shown in Fig. 17 with a size of 1.0 0.59 mm including all testing pads. Fig. 18 illustrates the circuit schematic of the -band magnetic coupled triple-cascode LNA. The device size of , , and is selected to be 24, 48, and 72 m, respectively. One

Fig. 21. Measured NF of the

-band LNA.

amplification stage with the noise-reduction transformers consisting of nH, nH, nH, and nH with [11] are adopted to achieve the high-gain, low-noise, and broadband performances.

YEH et al.: ANALYSIS AND DESIGN OF MMW LOW-VOLTAGE CMOS CASCODE LNA

Fig. 22. Simulated and measured: (a) small-signal gains and return losses and (b) reverse isolation and simulated stability factor of the -band LNA.

Fig. 23. Simulated and measured NF of the

-band LNA.

The transformers are designed based on (10)–(12), as mentioned in Section II-B. For saving chip area, small inductors are utilized to implement all the matching networks. The chip photograph

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Fig. 24. Simulated and measured: (a) small-signal gains and return losses and (b) reverse isolation and simulated stability factor of the -band magnetic coupled low-voltage triple-cascode LNA.

Fig. 25. Simulated and measured NF of the voltage triple-cascode LNA.

-band magnetic coupled low-

of the -band magnetic coupled triple-cascode LNA is shown in Fig. 19 with a size of 0.6 0.48 mm including all testing pads.

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TABLE II COMPARISON TABLE OF PREVIOUSLY REPORTED

-BAND LNAs AND THIS STUDY

bandwidth is not available B.W. stands for 3-dB bandwidth Chip size includes all testing pads by estimating Lowest measured NF

IV. MEASUREMENT A.

-Band LNA

This chip is measured via an on wafer ground–signal–ground (G–S–G) probe station and an Agilent network analyzer HP8510. Fig. 20 illustrates the simulated and on-wafer measured performances of the proposed -band LNA under 1.2-V supply. The simulation agrees with the measurement results. The -band LNA presents a peak gain of 13.8 dB at 37 GHz with a power consumption of 18 mW under 1.2-V supply voltage. When V, the power consumption decreases to 15 mW and the peak gain of the -band LNA is 13.3 dB at 37 GHz. When V, the power consumption becomes 12 mW and the peak gain of the -band LNA is 12.5 dB at 37 GHz. The 3-dB bandwidth ranges from 29 to 44 GHz. If the supply voltage varies from 1.2 to 0.8 V, the input and output return losses are all better than 10 dB and between 7–12 dB over the 3-dB bandwidth, respectively. Moreover, the reverse isolations are better than 36 dB in various supply voltages. If the supply voltage is 1.2 V, the measured is 10 dBm and is 1.7 dBm at 37 GHz.

Fig. 21 plots the simulated and measured NF from 26.5 to 50 GHz with various supply voltages. It is observed that under 1.2-V supply, the LNA exhibits a measured minimum NF of 3.8 dB at 37 GHz. From 26.5 to 50 GHz, the average NF is about 4.5 dB. Lowering to 0.8 V, the NF within the 3-dB bandwidth degrades about 0.3 dB. At 37 GHz, the measured output 1-dB compression point under 1.2-, 1.0-, and 0.8-V supply are 1.7, 1.0, and 0.9 dBm, respectively. Note that the measured is 1 dBm under 1.2-V supply at 37 GHz. B.

-Band LNAs

The chips are measured via an on-wafer G–S–G probe station and an Agilent network analyzer HP8510 with a -band test set. Fig. 22 shows the simulated and measured performances of the proposed -band magnetic coupled cascode LNA with a 1.2-V supply voltage. From Fig. 22, the simulation agrees with the measurement results over the operation frequency band. The measurement results show that the LNA exhibits a peak gain of 17.8 dB at 53.5 GHz under a 1.2-V supply with a power consumption of 19.2 mW. The 3-dB bandwidth ranges from 46 to 63 GHz. Over the 3-dB bandwidth, the input return loss is better than 10 dB

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TABLE III COMPARISON TABLE OF PREVIOUSLY REPORTED

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-BAND LNAs AND THIS STUDY

3-dB bandwidth 16 GHz B.W. stands for 3-dB bandwidth Lowest measured NF

and the output return loss is between 4.2–36 dB, respectively. Furthermore, the -band LNA has a peak gain of 17.8, 17.2, and 15.6 dB, whereas the power consumption is 19.2, 18, and 14.4 mW under 1.2, 1.0, and 0.8 V, respectively. The input return loss is better than 10 dB over 3-dB bandwidth even with the supply voltage is 1.2, 1.0, and 0.8 V. Moreover, the reverse isolations are better than 40 dB in various supply voltages. Note that the measured is 16 dBm and is 1 dBm at 60 GHz at 1.2 V. Fig. 23 illustrates the simulated and measured NF. It is observed that the measured NF is consistent with the simulation results. The LNA has a measured minimum NF of 4.4, 4.5, and 4.7 dB at 59.5 GHz under 1.2-, 1.0-, and 0.8-V supply voltage, respectively. The measured under 1.2-, 1.0-, and 0.8-V supply are 1, 1.2, and 4.1 dBm, respectively. The measured is also 9 dBm under a 1.2-V supply at 60 GHz. Fig. 24 shows the simulated and measured performances of the proposed -band magnetic coupled low-voltage triple-cascode LNA with a 1.2-V supply voltage. It is observed that the LNA exhibits a peak gain of 13.7 dB at 54 GHz with a power consumption of 14.4 mW. The 3-dB bandwidth ranges from 49 to 60 GHz. Over the 3-dB bandwidth, the input return loss is between 4.5–12.9 dB and the output return loss is between 5.5–11.9 dB, respectively. The small-signal gains, I/O return losses, and reverse isolations are also measured for the supply voltage of 1.2, 1.0, and 0.8 V. The -band magnetic coupled triple-cascode LNA has a peak gain of 13.7, 12.5, and 11.1 dB, whereas the power consumption is 14.4, 12, and 9.6 mW under 1.2, 1.0, and 0.8 V, respectively. The input and output return loss have little variations compared with the supply voltage is 1.2 V. Moreover, the reverse isolations are better than 32.5 dB in various supply voltages. The measured is 10 dBm and is 3.2 dBm with the supply voltage is 1.2 V at 54 GHz. Note that although the simulated -factor is 1.006 at

49 GHz in Fig. 24(b), the measured results [see Fig. 24(a)] do not show the instability. Fig. 25 shows the simulated and measured NF of the triplecascode LNA. It is observed that the measured NF is consistent with the simulation results. The LNA has a measured minimum NF of 5.3, 5.5, and 5.6 dB at 59.5 GHz under a 1.2-, 1.0-, and 0.8-V supply voltage, respectively. The measured under a 1.2, 1.0, and 0.8-V supply are 3.2, 1.5, and 0.8 dBm, respectively. The measured is also 4 dBm under a 1.2-V supply at 54 GHz. Tables I and II summarize the performances of the previous reported - and -band CMOS LNAs and our studies. From these tables, it is observed that the proposed - and -band LNAs have impressive performances in NF, power consumption, and larger gain bandwidth products, which are better than other published MMW LNAs reported to date. From Table II, our proposed -band LNAs have better noise performance compared with LNAs fabricated using a 65-nm CMOS process [6], [14]–[16], [23], whereas our proposed -band LNA in Table III features comparable performances with the cascode LNA fabricated using a 90-nm SOI CMOS process [27]. V. CONCLUSION In this paper, the magnetic coupled low-voltage multicascode topology has been presented, analyzed, and applied to implement three low-voltage cascode CMOS LNAs. Two with magnetic coupled cascode and triple-cascode configurations were designed at -band. The other with a one-stage magnetic coupled cascode configuration and a buffer stage was fabricated at -band in 90-nm technology. To minimize the NF, to maximize the small-signal gain, 3-dB bandwidth, and to minimize chip size, the noise-reduction transformers were designed and placed between the transistors of the cascode and the triple-cascode devices. The proposed magnetic coupled cascode LNA has

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a comparable noise performance compared with cascode LNA fabricated using a 65-nm CMOS process with a series inductor [6], whereas the magnetic coupled cascode LNA features lower supply voltage. Besides, the proposed magnetic coupled cascode and magnetic coupled triple-cascode LNAs has advantages of a better NF, larger gain bandwidth product, and lower supply voltage than the conventional cascode and triple-cascode LNAs. Based on this topology, the -band LNA has a gain of 13.8 dB and an NF of 3.8 dB at 37 GHz. The -band magnetic coupled cascode LNA has a gain of 17 dB at 57 GHz and a minimum NF of 4.4 dB at 59.5 GHz. Moreover, the -band magnetic coupled triple-cascode LNA presents a gain of 13.7 dB at 54 GHz and a minimum NF of 5.3 dB at 59.5 GHz. ACKNOWLEDGMENT The authors would like to thank Z.-Y. Liao, National Taiwan University, Taipei, Taiwan, for his helpful suggestions. The chip was fabricated by Taiwan Semiconductor (TSMC) through Chip Implementation Center of Taiwan. REFERENCES [1] J. H. Tsai, W. C. Chen, T. P. Wang, T. W. Huang, and H. Wang, “A miniature -band low noise amplifier using 0.13- m CMOS technology,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 6, pp. 327–329, Jun. 2006. [2] M. A. Masud, H. Zirath, M. Ferndahl, and H. O. Vickes, “90 nm CMOS MMIC amplifier,” in IEEE RFIC Symp. Dig., Jun. 2004, pp. 201–204. [3] S.-C. Shin, M.-D. Tsai, R.-C. Liu, K.-Y. Lin, and H. Wang, “A 24-GHz 3.9-dB NF low-noise amplifier using 0.18- m CMOS technology,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 7, pp. 448–450, Jul. 2005. [4] A. Liscidini, C. Ghezzi, E. Depaoli, G. Albasini, I. Bietti, and R. Castello, “Common gate transformer feedback LNA in a high IIP3 current mode RF CMOS front-end,” in IEEE Proc. CICC, Sep. 2006, pp. 25–28. [5] C.-C. Tang and S.-I. Liu, “Low-voltage CMOS low-noise amplifier using planar-interleaved transformer,” Electron. Lett., vol. 47, no. 8, pp. 497–498, Feb. 2001. [6] B.-J. Huang, H. Wang, and K.-Y. Lin, “Millimeter-wave low power and miniature CMOS multi-cascode low noise amplifiers with noise reduction topology,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 12, pp. 3049–3059, Dec. 2009. [7] K.-J. Sun, Z.-M. Tsai, K.-Y. Lin, and H. Wang, “A 10.8-GHz CMOS low-noise amplifier using parallel-resonant inductor,” in IEEE MTT-S Int. Microw. Symp. Dig., 2007, pp. 1795–1798. [8] H. C. Yeh, Z. Y. Liou, and H. Wang, “Analysis and design of millimeter-wave low power CMOS LNA with transformer-multi-cascode topology,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 12, pp. 3441–3454, Dec. 2011. [9] H.-C. Yeh, C.-C. Chiong, and H. Wang, “A low voltage -band CMOS LNA with magnetic coupled cascode topology,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012. [10] C.-M. Lo, C.-S. Lin, and H. Wang, “A miniature -band 3-stage cascode LNA in 0.13 m CMOS,” in Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2006, pp. 402–403. [11] P. C. Huang, Z. M. Tsai, K. Y. Lin, and H. Wang, “A 17–35 GHz broadband, high efficiency PHEMT power amplifier using synthesized transformer matching technique,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 1, pp. 112–119, Dec. 2012. [12] B. Razavi, “Design of millimeter-wave CMOS radios: A tutorial,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 56, no. 1, pp. 4–16, Jan. 2000. [13] P.-Y. Chang, S.-H. Su, S. S. H. Hsu, W.-H. Cho, and J.-D. Jin, “An ultra-low-power transformer-feedback 60 GHz low-noise amplifier in 90 nm CMOS,” IEEE Microw. Wireless Compon. Lett., vol. 22, no. 4, pp. 197–199, Apr. 2012.

[14] M. Varonen, M. Kärkkäinen, and K. A. I. Halonen, “Millimeter-wave amplifiers in 65-nm CMOS,” in Proc. 2007 Eur. Solid-State Circuit Conf., Sep. 2007, pp. 280–283. [15] A. Natarajan, S. Nicolson, M. D. Tsai, and B. Floyd, “A 60 GHz variable-gain LNA in 65 nm CMOS,” in Proc. IEEE Asian Solid-State Circuit Conf., 2008, pp. 117–120. [16] C. Weyers, P. Mayr, J. W. Kunze, and U. Langmann, “A 22.3 dB voltage gain 6.1 dB NF 60 GHz LNA in 65 nm CMOS with differential output,” in Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2008, pp. 192–193. [17] T. Yao, M. Q. Gordon, K. K. W. Tang, K. H. K. Yau, M. T. Yang, P. Schvan, and S. P. Voinigescu, “Algorithmic design of CMOS LNAs and PAs for 60-GHz radio,” IEEE J. Solid-State Circuits, vol. 42, no. 5, pp. 1047–1054, May 2007. [18] S. Pellerano, Y. Palaskas, and K. Soumyanath, “A 64 GHz 6.5 dB NF 15.5 dB gain LNA in 90 nm CMOS,” in Proc. Eur. Solid-State Circuit Conf., Sep. 2007, pp. 352–355. [19] J.-J. Lin, K.-H. To, B. Brown, D. Hammock, M. Majerus, M. Tutt, and W. M. Huang, “Wideband PA and LNA for 60-GHz radio in 90-nm LP CMOS technology,” in Compound Semiconduct. Integr. Circuits Symp., Oct. 2008, pp. 1–4. [20] C. H. Doan, S. Emami, A. M. Niknejad, and R. W. Brodersen, “Millimeter-wave CMOS design,” IEEE J. Solid-State Circuits, vol. 40, no. 1, pp. 144–155, Jan. 2005. [21] M. Varonnen, M. Karkkainen, M. Kantanen, and K. Halonen, “Millimeter-wave integrated circuits in 65-nm CMOS,” IEEE J. Solid-State Circuits, vol. 43, no. 9, pp. 1991–2002, Sep. 2008. [22] W.-H. Lin, J.-H. Tsai, Y.-N. Jen, T.-W. Huang, and H. Wang, “A 0.7-V 60-GHz low-power LNA with forward body bias technique in 90 nm CMOS process,” in Eur. Microw. Conf., Paris, France, Sep. 2009, pp. 393–396. [23] F. Vecchi, S. Bozzola, E. Temporiti, D. Guermandi, M. Pozzoni, M. Repossi, M. Cusmai, U. Decanis, A. Mazzanti, and F. Svelto, “A wideband receiver for multi-Gbit/s communications in 65 nm CMOS,” IEEE J. Solid-State Circuits, vol. 46, no. 3, pp. 1044–1057, Mar. 2011. [24] N. Li, K. Bunsen, N. Takayama, Q. Bu, T. Suzuki, M. Sato, T. Hirose, K. Okada, and A. Matsuzawa, “A 24 dB gain 51–68 GHz CMOS low noise amplifier using asymmetric-layout transistors,” in IEEE Eur. Solid-State Circuits Conf., Seville, Spain, Sep. 2010, pp. 342–345. [25] K.-J. Sun, Z.-M. Tsai, K.-Y. Lin, and H. Wang, “A noise optimization formulation for CMOS low-noise amplifiers with on-chip lowinductors,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 4, pp. 1554–1560, Apr. 2006. [26] H. Shigematsu, T. Hirose, F. Brewer, and M. Rodwell, “Millimeterwave CMOS circuit design,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 2, pp. 472–477, Feb. 2005. [27] F. Ellinger, “26–42 GHz SOI CMOS low noise amplifier,” IEEE J. Solid-State Circuits, vol. 39, no. 3, pp. 522–528, Mar. 2004. [28] P. Sakian, E. Janssen, A. H. M. van Roermun, and R. Mahmoudi, “Analysis and design of a 60 GHz wideband voltage-voltage transformer feedback LNA,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 3, pp. 702–713, Mar. 2012. [29] H.-S. Oh, J. Jeong, C. D. Presti, A. Scuderi, and P. M. Asbeck, “A watt-level stacked-FET linear power amplifier in silicon-on-insulator CMOS,” IEEE Trans. Microw. Theory Techn., vol. 10, no. 1, pp. 57–64, Jan. 2010. [30] V. Giammello, E. Ragonese, and G. Palmisano, Transformer-Coupled Cascode Stage for mm-wave Power Amplifiers in Sub- m CMOS Technology, ser. Analog Integr. Circuits Signal Process.. Berlin, Germany: Springer, 2011, vol. 66, pp. 449–453.

Han-Chih Yeh (S’11) was born in Taichung, Taiwan, on January 30, 1981. He received the B.S. degree in civil engineering and M.S. degree in communication engineering, from National Taiwan University, Taipei, Taiwan, in 2005 and 2007, respectively, and is currently working toward the Ph.D. degree at National Taiwan University. His research interests include microwave and MMW integrated-circuit designs.

YEH et al.: ANALYSIS AND DESIGN OF MMW LOW-VOLTAGE CMOS CASCODE LNA

Chau-Ching Chiong (S’11) was born in Taipei, Taiwan, in 1974. He received the B.S. and M.S. degrees in electrical engineering from National Taiwan University, Taipei, Taiwan, in 1997 and 1999, respectively, and the Ph.D. degree in astronomy from the University of Bonn, Bonn, Germany, in 2003. He then joined the Institute of Astronomy and Astrophysics, Academia Sinica (ASIAA), Taipei, Taiwan, where he is involved in research and development of the Atacama Large Millimeter Array (ALMA) project. His current research interests include large-array and focal-plane array receiver systems and very low-noise systems in radio astronomical applications using MMICs.

Sofiane Aloui received the Master degree from the Electrical Engineering School, University of Rennes, Rennes, France, in 2005, and the Ph.D. degree from the University of Bordeaux, Bordeaux, France, in 2010. In 2006, he joined the French Research Agency (CNRS), as a doctoral student. His doctoral activities took place at IMS, the Microelectronics Laboratory, University of Bordeaux. His research was focused on the design of millimeter-wave CMOS power amplifiers. From August 2011 to August 2012, he was a Postdoctoral Research Fellow with the Graduate Institute of Communication Engineering, National Taiwan University. He is currently an Assistant Professor with the Electrical Engineering School, Ecole Nationale Superieure de l’Electronique et de ses Applications (ENSEA), Cergy-Pontoise, France. He is involved with the design of broadband low-cost transceivers dedicated for chip-to-chip communications in the context of system-on-chip (SoC) and network-on-chip (NoC). Dr. Aloui was the recipient of the Best Paper Award of the 2010 IEEE Latin American Symposium in Circuits and Systems (LASCAS) Conference.

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Huei Wang (S’83–M’87–SM’95–F’06) was born in Tainan, Taiwan, on March 9, 1958. He received the B.S. degree in electrical engineering from National Taiwan University, Taipei, Taiwan, in 1980, and the M.S. and Ph.D. degrees in electrical engineering from Michigan State University, East Lansing, in 1984 and 1987, respectively. During his graduate study, he was engaged in research on theoretical and numerical analysis of electromagnetic radiation and scattering problems. He was also involved in the development of microwave remote detecting/sensing systems. In 1987, he joined the Electronic Systems and Technology Division, TRW Inc. He has been an MTS and Staff Engineer responsible for MMIC modeling of computer-aided design (CAD) tools, MMIC testing evaluation, and design, and became the Senior Section Manager of the Millimeter-Wave Sensor Product Section, RF Product Center. In 1993, he visited the Institute of Electronics, National Chiao-Tung University, Hsin-Chu, Taiwan, to teach MMIC-related topics. In 1994, he returned to TRW Inc. In February 1998, he joined the faculty of the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, as a Professor. From Aug. 2006 to July 2009, he was the Director of the Graduate Institute of Communication Engineering, National Taiwan University. From 2005 to 2007, he was the Richard M. Hong Endowed Chair Professor of National Taiwan University. He is currently a National Chair Professor of the Ministry of Education, Taiwan, ROC (February 2011–January 2014 term). Dr. Wang is a member of Phi Kappa Phi and Tau Beta Pi. He was an IEEE Distinguished Microwave Lecturer (2007–2009). He was the recipient of the 2003 Distinguished Research Award of the National Science Council, Taiwan, the 2007 Academic Achievement Award of the Ministry of Education, Taiwan, and the 2008 Distinguished Research Award of the Pan Wen-Yuan Foundation.

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4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers Beatriz Aja Abelán, Member, IEEE, Matthias Seelmann-Eggebert, Daniel Bruch, Arnulf Leuther, Hermann Massler, Boris Baldischweiler, Michael Schlechtweg, Juan Daniel Gallego-Puyol, Member, IEEE, Isaac López-Fernández, Carmen Diez-González, Inmaculada Malo-Gómez, Enrique Villa, and Eduardo Artal

Abstract—In this paper, monolithic microwave integrated circuit (MMIC) broadband low-noise amplifiers (LNAs) for cryogenic applications based on a 100-nm metamorphic high-electron mobility transistor (mHEMT) technology in combination with grounded coplanar waveguide are reported. A three-stage LNA, operating in 4–12 GHz and cooled to 15 K exhibits an associated gain of 31.5 dB 1.8 dB and average noise temperature of 5.3 K dB with a low power dissipation of 8 mW. Additionally another three-stage LNA 25–34 GHz cooled to 15 K 0.4 dB with 15.2 K has demonstrated a flat gain of 24.2 dB dB , average noise temperature, with a very low power dissipation of 2.8 mW on chip. The mHEMT-based LNA MMICs have demonstrated excellent noise characteristics at cryogenic temperatures for their use in radio-astronomy applications. Index Terms—Cryogenic low-noise amplifier (LNA), metamorphic high electron-mobility transistor (mHEMT), monolithic microwave integrated circuit (MMIC).

I. INTRODUCTION

A

NEW generation of focal plane arrays, with a large number of pixels, enhance the mapping efficiency of some of the existent radio telescopes. This need of a large number of receivers has been the initial motivation for the development of monolithic microwave integrated circuits (MMICs) especially designed to obtain good cryogenic performance. Cryogenic low-noise amplifiers (LNAs) working at 4–15-K ambient temperature are the key component in the front-ends of all those ultra-low-noise cryogenic receivers used for radio astronomy and deep-space communications. For such a large number of LNAs, MMICs enable simple, Manuscript received July 10, 2012; revised September 13, 2012; accepted September 14, 2012. Date of publication November 12, 2012; date of current version December 13, 2012. This work was supported by the Ministerio de Ciencia e Innovación under Research Program Grant TRA2009-0304. This work was supported in part by the Instituto Geográfico Nacional and the IAF-Fraunhofer funds. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. B. Aja Abelán, E. Villa, and E. Artal are with the Department of Communications Engineering, University of Cantabria, Santander 39005, Spain (e-mail: [email protected]). M. Seelmann-Eggebert, D. Bruch, A. Leuther, H. Massler, B. Baldischweiler, and M. Schlechtweg are with the Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg 79108, Germany (e-mail: [email protected]). J. D. Gallego-Puyol, I. López-Fernández, C. Diez-González, and I. Malo-Gómez are with the Centro Astronómico de Yebes, Centro de Desarrollos Tecnológicos (CDT), Instituto Geográfico Nacional (IGN), Guadalajara 19080, Spain (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2221735

small size, and low-cost production. These LNAs should be designed to obtain the lowest possible noise. Moreover, some of the radio-astronomy applications also require a very wide instantaneous bandwidth in order to increase the sensitivity of continuum observations. In that case, gain fluctuations of the amplifier may play a role since they can degrade the sensitivity. To date, InP pseudomorphic high electron-mobility (pHEMT) MMIC LNAs have demonstrated outstanding noise at cryogenic temperatures [1]–[6]. However, recently metamorphic high electron-mobility transistor (mHEMT)-based LNAs have also been reported with good performances [7]–[10]. The advantages of mHEMT technology are lower costs, better robustness, and availability of larger GaAs wafers for production compared to InP substrate materials. The potential of the 100-nm mHEMT technology for MMIC applications at cryogenic temperatures is evaluated in this paper. We report the results obtained in two designs for the 4–12- and 25–34-GHz bands. The 4–12-GHz band is of great interest since it is typically used in the IF of millimeter- and submillimeter-wave cryogenic receivers. The mixing element in this type of receiver is a superconducting–insulating–superconducting (SIS) junction, a superconducting hot-electron bolometer (HEB), or a Schottky-barrier diode, cryogenically cooled to 4 K. The 25–34-GHz band is very important in very long baseline interferometry (VLBI) for astronomy and geodesy observation (see VLBI 2010 [11]), as well as for the down link of modern deep-space missions [12]. After a description of the technology in Section II, the device modeling with ambient and cryogenic measurements is shown in Section III. Circuit designs are discussed in Section IV, and their characterization at room and cryogenic temperatures is described in Section V. II. mHEMT TECHNOLOGY For ultra-low-noise applications, high electron-mobility transistors (HEMTs) based on InGaAs/InAlAs heterostructures with high In-content in the electron transport channel are the most appropriate devices [13]. These heterostructures can be grown either directly on InP wafers or by using a metamorphic buffer to adapt the lattice constant on GaAs substrates. Major advantages of the metamorphic approach are cost and quality of the GaAs wafers. Furthermore, the material is less brittle compared to InP. The InAlAs/InGaAs epi-structure is grown by molecular beam epitaxy (MBE) on 4-in semi-insulating GaAs substrates. For the metamorphic buffer, a 1- m-thick linear

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Fig. 2. Cryogenic probe station. Fig. 1. SEM cross section of a 100-nm mHEMT.

InxAl Ga As transition is used. The Ga As/In Ga As split electrons are confined in a In channel to increase the breakdown voltage. The low-energy electrons are confined in the In Ga As layer with high electron mobility. In addition, the high-energy electrons are distributed over both layers, which reduces impact ionization. The Al As barriers. The upper split channel is confined by In barrier layer includes a silicon doping. The layer sequence is capped with a highly doped In Ga As layer to reduce the ohmic contact and source resistance. A wet chemically mesa etch process is used for device isolation. The InGaAs channel layer is under-etched to avoid contact between the conducting InGaAs channel material and the gate metallization crossing the mesa edge in order to avoid gate leakage currents. Electron beam evaporated GeAu layers are used for the ohmic contacts, which are alloyed at 300 C on a nitrogen purged hot plate. The 100-nm T gate is defined by 100-kV electron-beam lithography using a three-layer resist (PMMA). The gate recess is etched with a succinic-acid-based solution. Great care is taken to achieve homogeneous lateral etching across the 4-in wafer. An undersized lateral recess width would degrade the breakdown voltage of the device, whereas an oversized lateral recess would increase the source resistance [14]. A Pt Ti Pt–Au layer sequence is used for the gate metallization. The active devices feature T-shaped 100-nm gates with an indium content of 65% in the main channel. A cross section of a realized 100-nm transistor is shown in Fig. 1. These devices also of 220 GHz and a of 300 GHz. A twotypically have a finger device with 0.06-mm total gate width is used for process monitoring. Typical values are a maximum transconductance of 1400 mS/mm with a drain bias of 1 V and a two-terminal reverse breakdown greater than 4 V at ambient temperature. The transmission lines used in the MMICs are grounded coplanar waveguides with two metallization levels and 3- m Au thickness. The process further includes 50- /sq NiCr thin-film resistors, 225 pF/mm metal–insulator–metal (MIM) capacitors, via-holes, and CVD SiN passivation.

Fig. 3. I–V characteristics for a 4 15 m mHEMT device at 15 K (blue in online version) and at 300 K (red in online version) for several gate voltages.

The wafers are thinned down to a final thickness of 50 m. The 100-nm gate-length HEMT devices exhibited more than 90% yield for the fabricated wafers. III. DEVICE MODELING The design of cryogenic LNAs requires a small-signal HEMT model with noise parameters; therefore, it was developed first [15]. The -parameters of the device, both at ambient temperature 300 and 15 K, were measured on a wafer using a thrureflect line (TRL) calibration, in the cryogenic probe station shown in Fig. 2. From these measurements, parasitic elements and intrinsic capacitances were determined. The noise parameters of the transistors were modeled following the approach of Pospieszalski [16]. Cryogenic models were improved based on the data from numerous runs. DC measurements were carried out at 300 and 15 K on a representative device with gate length of 100 nm and gate width of 4 15 m. The output I–V characteristics are shown in Fig. 3. The device exhibits good pinch-off characteristics. The kink effect appears at around 15 K V.

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Fig. 6. Schematic diagram of the 4–12-GHz MMIC LNA.

Fig. 4. Transconductance and characteristics for a 4 mHEMT device at 15 and 300 K for several drain voltages.

15 m

Fig. 7. Photograph of the manufactured 4–12-GHz MMIC LNA. The chip size is 2.5 mm 1 mm.

A. LNA 4–12 GHz

Fig. 5. Gate current–voltage characteristics for a 4 at 15 and at 300 K for several gate voltages.

15 m mHEMT device

The transconductance and characteristics for the same device are plotted in Fig. 4. The device exhibits a maximum transconductance of 1500 mS/mm with V at 15 K and 1400 mS/mm with V at 300 K. The gate leakage current is an important parameter related to the noise behavior of the device. Measured characteristics are shown in Fig. 5. The gate leakage at 15 K is lower than at 300 K, in the range of a few nanoamperes for from 0.2 to 0.2 V and from 0.1 to 0.9 V. The device -parameters were also measured on wafer at both ambient temperature 300 and 15 K up to 50 GHz. Measurement results can be found in [15] and [17]. IV. AMPLIFIERS DESIGN To demonstrate the potential of the mHEMT technology at cryogenic temperatures, two MMIC LNAs were designed and manufactured. The two single-ended LNAs cover the frequency range from 4 to 12 GHz (IF for millimeter-wave receivers) and from 25- to 34-GHz VLBI and deep-space bands), respectively.

A simplified schematic of the three-stage 4–12-GHz LNA is shown in Fig. 6. The LNA has three stages, which include 4 30 m transistors. A photograph of the three-stage 4–12-GHz LNA is shown in Fig. 7. The chip size is 2.5 mm 1 mm. The first stage is mainly optimized for minimum noise figure, while the second stage is matched partially for noise, and the third stage fully for gain. Gain flatness and input and output reflection coefficients were also taken into account during the design optimization. Grounded coplanar-waveguide lines are used for matching networks and interconnections. Bias is brought to the transistors through resistors and stubs capacitively shorted with RF bypass MIM capacitors. The resistors act as damping elements suppressing the excess out-of-band gain and stabilizing the amplifier. Matching the first transistor for minimum noise requires a high impedance of about 100 real part with low losses. An external matching network, on a low-loss substrate, allows more flexibility to match the optimum noise impedance to the source impedance at these frequencies. Therefore, an external microstrip input matching network has been designed as shown Fig. 8, which is fabricated on a 0.254-mm CLTE-XT Arlon substrate with lower losses than GaAs, and the inductance is realized by one 1.6-mm-long bond wire. This network allows to achieve broadband matching, to reduce the circuit noise figure, and to tune the amplifier. The first gate is biased through the RF input, and this is done through the external input matching network. In order to characterize its performance, the MMIC was assembled in a gold-plated brass module with SMA coaxial connectors, shown in Fig. 9.

AJA ABELÁN et al.: 4–12- AND 25–34-GHz CRYOGENIC mHEMT MMIC LNAs

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Fig. 11. Photograph of the manufactured 25–34-GHz MMIC LNA. The chip size is 2.5 mm 1 mm.

Fig. 8. Schematic diagram of a 4–12-GHz MMIC LNA with the external input matching network.

Fig. 12. Packaged module of the 25–34-GHz LNA. The dimensions of the box are 20.6 mm 32.5 mm 12 mm.

Fig. 9. Packaged module of the 4–12-GHz LNA. The box dimensions are 31.3 mm 40 mm 15 mm.

networks are used both for interstage matching and for biasing the drains. A photograph of the three-stage LNA is shown in Fig. 11. The chip size is 2.5 mm 1 mm. The LNA MMIC was assembled in a gold-plated aluminium module with 2.92-mm coaxial connectors, shown in Fig. 12. Gold-plated microstrip lines on a 0.127-mm CLTE-XT Arlon dielectric substrate were used at the input and output of the MMIC. V. EXPERIMENTAL RESULTS

Fig. 10. Schematic diagram of the 25–34-GHz MMIC LNA.

B. LNA 25–34 GHz As is shown in Fig. 10, the MMIC LNA consists of three stages; each one employs a 4 15 m transistor, with a source inductive stub in the two first stages. Grounded coplanarwaveguide lines are used for matching networks and interconnection. To accomplish wideband matching, lossy matching

-parameters, noise temperature, and gain fluctuations were tested at 300- and 15-K temperatures. The chips were first tested on-wafer and then the packaged LNAs were measured at 300 and 15 K. The characterization at cryogenic temperatures of the modules was carried out in a closed-cycle helium cryostat, partially shown in Fig. 13. For both amplifiers, two units were packaged and tested at cryogenic temperatures in order to verify the measurements. Test results demonstrated very good repeatability, and therefore that the process is sufficiently stable. Moreover, the amplifiers

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Fig. 15. Measured and simulated gain and noise temperature of the LNA 4–12 GHz at 15 K.

Fig. 13. Amplifier inside the vacuum chamber of the cryostat test system.

Fig. 16. Measured and simulated -parameters of the LNA 4–12 GHz at 15 K. Fig. 14. Measured and simulated gain and noise temperature of the LNA 4–12 GHz at 300 K.

were unconditionally stable at both room and cryogenic temperatures, which was checked from the -parameter measurement. A. LNA 4–12 GHz The 4–12-GHz amplifier was tested at room temperature and it exhibited the gain and noise temperature depicted in Fig. 14. The measured gain was 38 dB with ripple of 1.6 dB in the 4–12-GHz frequency band and with average noise of 47.8 K. The on-chip power consumption for this optimum noise bias was 90.2 mW; V, mA (166 mA/mm). The minimum noise was 35 K with an associated gain of 37.7 dB at 7.75 GHz. At 15 K, the cold attenuator method was used to measure the LNA module noise performance, where the incoming noise power is generated by a commercial noise source. A cooled 15-dB attenuator provides a well-defined cold-temperature noise reference at the input of the LNA and reduces the change of reflection coefficient between the on- and off-states of the noise source. In this way, the measurement uncertainty of the noise temperature is reduced to 1.4 K.

The measured and simulated gain and noise temperature at 15 K from 3 to 13 GHz are shown in Fig. 15. The simulation comprises the MMIC LNA, as well as the external microstrip network and coaxial connectors. From 4 to 12 GHz, the amplifier achieves 31.5-dB gain with 1.8-dB flatness. The average noise temperature is 5.3 K from 4 to 12 GHz. The measurement was made with a drain voltage V and a total drain current of 15 mA (41.6 mA/mm). The dc power dissipation is 8 mW on-chip. The minimum noise temperature is 4 K at 6.25 GHz with 30 dB of gain. The LNA -parameters at cryogenic temperature (15 K) were also measured referred to the input and output ports of the packaged amplifier for the same bias conditions as in the measurement achieving the best noise performance, shown in Fig. 16. Input and output return losses are greater than 5 and 14 dB in the band, respectively (the input reflection loss (IRL) is greater than 12 dB from 5 to 12 GHz). B. LNA 25–34 GHz After testing the -parameters of the chip on-wafer at room temperature, it was also tested in the cryogenic probes station at 15 K. The -parameters at 15 K are shown in Fig. 17. With

AJA ABELÁN et al.: 4–12- AND 25–34-GHz CRYOGENIC mHEMT MMIC LNAs

Fig. 17.

-parameters on-wafer of the LNA 25–34 GHz at 15 K.

Fig. 18. Measured and simulated gain and noise temperature of the packaged LNA 25–34 GHz at 300 K.

a power dissipation of 3.6 mW, V and a total current of 9.0 mA (50 mA/mm), the gain was 24.3 dB with a ripple of only 0.3 dB. Input and output return losses were greater than 15 and 20 dB in the band, respectively. The amplifier was then measured in the module with coaxial connectors at 300 K. The gain and noise temperature are depicted in Fig. 18. The measured gain was 25.2 dB with ripple of 0.8 dB in the 25–34-GHz frequency band. The average noise in the band was 190 K with a power dissipation of 17.3 mW on chip; V, mA (141 mA/mm). The minimum noise temperature was 183 K at 29 GHz, with an associated gain of 25 dB. Next, the noise performance was measured with the amplifier cooled to cryogenic temperature. The measured and simulated gain and noise temperature from 20 to 40 GHz at 15 K are shown in Fig. 19. The simulation includes the amplifier with bonding wires, microstrip lines, and coaxial connectors. The gain and noise were tested using the cold attenuator method. The measured gain was 24.2 dB with a ripple of 0.4 dB in the 25–34-GHz frequency band and the average noise in the band was 15.2 K.

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Fig. 19. Measured and simulated gain and noise temperature of the packaged LNA 25–34 GHz at 15 K.

Fig. 20. Measured gain and noise temperature of the packaged LNA 25–34 GHz at 15 K, using the cold attenuator (CA) method with a diode as noise source, and the hot/cold method (HL) with a 50- load at the input of the amplifier.

The minimum noise temperature was 11.8 K with an associated gain of 24.5 dB at 29.5 GHz. The power consumption was 2.8 mW on chip; V and mA (42 mA/mm). An identical LNA from the same wafer was also assembled and tested at cryogenic temperature using two different methods in order to verify the measurements of noise and gain. The methods were: 1) the cold attenuator method with a diode noise source and 2) the hot/cold method with a 50- load at the input of the amplifier [18]. The results obtained in gain and noise temperature for both methods are shown in Fig. 20. The gain was the same, 25.3 0.6 dB and the average temperature 16.6 K with the cold-attenuator method, and 14.9 K with the hot/cold method, showing a difference in the average temperature of only 1.7 K. In addition, the hot/cold method showed a smoother response of the noise temperature versus frequency. One of the possible applications of this amplifier is in the front end of cosmic microwave background (CMB) radiation receivers [19], [20]. The very wide band of those receivers combined with the extreme low noise makes the problem of gain fluctuations more prominent. The gain fluctuation of the LNA

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HERSCHEL [22], achieving SNFG values at 1 Hz lower than those obtained for cryogenic InP amplifiers [23]. A comparison of the two LNAs with other reported wideband MMIC LNAs, working in the same frequency ranges at cryogenic temperature, is given in Table I. Almost all data found in the literature refer to InP-based devices. Both presented LNAs offer very low-noise performance with ultra-low-power dissipation at cryogenic temperatures. VI. CONCLUSION

Fig. 21. Normalized gain fluctuation spectrum of the LNA 25–34 GHz at 15 K. The dashed line indicates the noise floor of the measurement system.

TABLE I COMPARISON OF WIDE-BANDWIDTH LNA AT CRYOGENIC TEMPERATURE

Ultra-low-noise MMIC LNAs that can operate cryogenically cooled are required for radio-astronomy applications. We reported the fabrication and characterization of two MMIC LNAs based on 100-nm mHEMT technology. These very low-noise and wide instantaneous bandwidth amplifiers have been developed in order to demonstrate the excellent performance of this mHEMT technology at cryogenic temperatures. Their performance has been characterized in terms of small-signal gain and equivalent noise temperature under cryogenic operating conditions (15 K). A three-stage LNA demonstrated a small-signal gain of 31.5 dB and average noise temperature of 5.3 K from 4 to 12 GHz when cooled at 15 K with only 8.0-mW power consumption. The 25–34-GHz MMIC LNA exhibited a gain of 24.2 dB and average noise temperature of 15.2 K with 2.8-mW power consumption. Both LNAs offer very low-noise performance with very low-power dissipation at cryogenic temperatures. The presented results demonstrate the high potential of mHEMT technology for cryogenically cooled very sensitive wideband receivers. ACKNOWLEDGMENT The authors would like to thank all the people involved in manufacturing the prototypes used in this study. The authors express their gratitude to the Technology Department, Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg, Germany, for the epitaxial growth and wafer processing.

Narrowband design with cooled at 12 K.

K and Gain

dB at 32 GHz when

25–34 GHz operating cryogenically was measured as described in [21]. The spectrum of normalized gain fluctuation (SNGF) measured is shown in Fig. 21. The SNFG is usually modeled by an expression of the form [21] Hz

(1)

is the unilateral spectral density (i.e., SNGF) with where units Hz . In cryogenic LNAs, the parameter is usually close to 0.5. The best fit to the data shown in Fig. 21 is obtained with Hz and . These results would meet the stringent specifications of Atacama Large Millimeter/Sub-millimeter Array (ALMA)1 or 1ALMA, Santiago, Chile. [Online]. Available: http://www.almaobservatory. org/

REFERENCES [1] J. Randa, E. Gerecht, D. Gu, and R. L. Billinger, “Precision measurement method for cryogenic amplifier noise temperatures below 5 K,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 3, pp. 1180–1189, Mar. 2006. [2] J. D. Pandian, L. Baker, G. Cortes, P. F. Goldsmith, A. A. Deshpande, R. Ganesan, J. Hagen, L. Locke, N. Wadefalk, and S. Weinreb, “Low noise 6–8 GHz receiver,” IEEE Microw. Mag., vol. 7, no. 6, pp. 74–84, Dec. 2006. [3] Y.-L. Tang, N. Wadefalk, M. A. Morgan, and S. Weinreb, “Full -band high performance InP MMIC LNA module,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 81–84. [4] J. J. Bautista, J. G. Bowen, N. E. Fernandez, Z. Fujiwara, J. Loreman, S. Petty, S. J. L. Prater, R. Grunbacher, R. Lai, M. Nishimoto, M. R. Murti, and J. Laskar, “Cryogenic, -band and -band InP HEMT based LNAs for the deep space network,” in IEEE Aerosp. Conf., Mar. 2001, vol. 2, pp. 829–842. [5] D. Kettle, N. Roddis, and R. Sloan, “A lattice matched InP chip set for a band radiometer,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 1033–1036. [6] J. Schleeh, N. Wadefalk, P. Nilsson, P. Starski, G. Alestig, J. Halonen, B. Nilsson, A. Malmros, H. Zirath, and J. Grahn, “Cryogenic 0.5–13 GHz low noise amplifier with 3 K midband noise temperature,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3.

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[7] A. Leuther, A. Tessmann, I. Kallfass, R. Losch, M. Seelmann-Eggebert, N. Wadefalk, F. Schafer, J. D. G. Puyol, M. Schlechtweg, M. Mikulla, and O. Ambacher, “Metamorphic HEMT technology for low-noise applications,” in IEEE Int. Indium Phosphide Relat. Mater. Conf., 2009, pp. 188–191. [8] B. Aja, K. Schuster, F. Schafer, J. D. Gallego, S. Chartier, M. Seelmann-Eggebert, I. Kallfass, A. Leuther, H. Massler, M. Schlechtweg, C. Diez, I. Lopez-Fernandez, S. Lenz, and S. Turk, “Cryogenic lownoise mHEMT-based MMIC amplifiers for 4–12 GHz band,” IEEE Microw. Wireless Compon. Lett., vol. 21, no. 11, pp. 613–615, Nov. 2011. [9] S.-H. Weng, H.-Y. Chang, C.-C. Chiong, and M.-T. Chang, “Cryogenic evaluation of a 30–50 GHz 0.15- m MHEMT low noise amplifiers for radio astronomy applications,” in Proc. 41st Eur. Microw. Conf., Oct. 2011, pp. 934–936. [10] B. Aja, M. Seelmann-Eggebert, A. Leuther, H. Massler, M. Schlechtweg, C. Diez, J. D. Gallego, I. Lopez-Fernandez, I. Malo, E. Artal, and E. Villa, “4–12 GHz and 25–34 GHz cryogenic MHEMT MMIC low noise amplifiers for radio astronomy,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [11] A. Niell, A. Whitney, B. Petrachenko, W. Schlüter, N. Vandenberg, H. Hase, Y. Koyama, C. Ma, H. Schuh, and G. Tuccari, “VLBI2010: Current and future requirements of geodetic VLBI systems,” NASA, Washington, DC, Int. VLBI Service for Geodesy and Astrometry 2005 Annu. Rep. NASA/TP-2006-214136, 2006, pp. 13–40. [Online]. Available: ftp://ivscc.gsfc.nasa.gov/pub/ annual-report/2005/pdf/spcl-vlbi2010.pdf, D. Behrend and K. Baver, Eds. [12] E. Vassallo, R. Martin, R. Madde, M. Lanucara, P. Besso, P. Droll, G. Galtie, and J. De Vicente, “The European Space Agency’s deepspace antennas,” Proc. IEEE, vol. 95, no. 11, pp. 2111–2131, Nov. 2007. [13] L. Samoska, “Towards terahertz MMIC amplifiers: Present status and trends,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 333–336. [14] K. Shinohara, Y. Yamashita, A. Endoh, K. Hikosaka, T. Matsui, S. Hiyamizu, and T. Mimura, “Importance of gate-recess structure to the cutoff frequency of ultra-high-speed InGaAs/InAlAs HEMTs,” in 14th Indium Phosphide Relat. Mater., 2002, pp. 451–454. [15] M. Seelmann-Eggebert, F. Schaefer, A. Leuther, and H. Massler, “A versatile and cryogenic mHEMT-model including noise,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2010, pp. 501–504. [16] M. W. Pospieszalski, “Modeling of noise parameters of MESFET’s and MODFET’s and their frequency and temperature dependence,” IEEE Trans. Microw. Theory Techn., vol. 37, no. 9, pp. 1340–1350, Sep. 1989. [17] M. Seelmann-Eggebert, A. Leuther, H. Maßler, B. Aja, D. Bruch, A. Tessmann, I. Kallfass, and M. Schlechtweg, “The IAF mHEMT low-noise technology and its extension to cryogenic applications,” presented at the 1st Eng. Forum Workshop, Göteborg, Sweden, Jun. 23–24, 2009. [18] D. Bruch, F. Schafer, B. Aja, A. Leuther, M. Seelmann-Eggebert, I. Kallfass, M. Schlechtweg, and O. Ambacher, “A single chip broadband noise source for noise measurements at cryogenic temperatures,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2011, pp. 1–4. [19] M. Bersanelli et al., “Planck pre-launch status: Design and description of the low frequency instrument,” Astron. Astrophys., vol. 520, Oct. 2010, Art. ID AN. A4. [20] J. A. Rubiño-Martin et al., “The QUIJOTE CMB experiment,” in Highlights of Spanish Astrophysics V, Astrophysics and Space Science Proceedings. Berlin, Germany: Springer, 2010, pt. 3, pp. 127–135. [21] J. D. Gallego, I. López-Fernández, C. Diez, and A. Barcia, “Methods for the characterization and measurement of the gain fluctuations of cryogenic amplifiers,” ALMA, Santiago, Chile, ALMA Memo 560, Oct. 2006. [Online]. Available: http://www.alma.nrao.edu/memos/ html-memos/alma560/memo560.pdf. [22] T. de Graauw et al., “The Herschel-Heterodyne Instrument for the farinfrared (HIFI),” Astron. Astrophys., vol. 518, L6, pp. 1–7, Jul.–Aug. 2010. [23] I. López-Fernández, J. D. Gallego, C. Diez, A. Barcia, and J. M. Pintado, “Wide band, ultra low noise cryogenic InP IF amplifiers for the Herschel mission radiometers,” Proc. SPIE, vol. 4855, pp. 489–500, 2003.

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Beatriz Aja Abelán (S’01–A’05–M’06) received the Telecommunications Engineering degree and Ph.D. degree from the University of Cantabria, Santandar, Spain, in 1999 and 2007 respectively. Since 1999, she has been with the Department of Communications Engineering, University of Cantabria. From 2008 to 2012, she was an Invited Scientist with the Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg, Germany, in a joint collaboration project with Centro Astronómico de Yebes (CAY). Her research interests are in the area of microwave and millimeter-wave circuits and systems design, in particular the design of microwave LNAs for cryogenic applications.

Matthias Seelmann-Eggebert received the Diploma and Ph.D. degree in physics from the University of Tübingen, Tübingen, Germany, in 1980 and 1986, respectively. From 1980 to 1996, he was involved in research and development related to infrared detectors based on HgCdTe and applied research in the field of electrochemistry and surface physics. From 1990 to 1991, he was a Visiting Scientist with Stanford University, Stanford, CA. From 1997 to 2000, he was engaged in the growth of CVD diamonds. Since 2001, he has been a member of the High Frequency Devices and Circuits Department, Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg, Germany, where he is in charge of the development of linear and nonlinear compact models for III–V devices.

Daniel Bruch was born in 1982. He received the Dipl.-Ing. degree from the University of Karlsruhe, Karlsruhe, Germany, in 2008, and is currently working toward the Ph.D. degree at the Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg, Germany. His main research interests are the design and characterization of cryogenic LNAs.

Arnulf Leuther received the Dipl. Phys. degree and Ph.D. degree in physics from the Technical University of Aachen, Aachen, Germany. From 1992 to 1996, he was with Forschungszentrum Jülich. In 1996, he joined the Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg, Germany. where he is currently Head of the Lithography Group. His research is focused on the development of advanced III–V process technologies for metamorphic HEMTs and the fabrication of millimeter- and submillimeter-wave MMICs. Dr. Leuther received the 1996 Borchert Medal from RWTH Aachen for his dissertation thesis.

Hermann Massler was born in Radolfzell, Germany, in 1965. He studied electrical engineering at the Technical University Karlsruhe, Karlsruhe, Germany, where he graduated in 1993. While working on the Diploma degree at the Forschungszentrum Karlsruhe (FZK), he performed and investigated quasi-optical measurements at 140 GHz. He continued these studies as an FZK Research Assistant for an additional year. Since 1994, he has been with the Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg, Germany, where he is involved with transistor and integrated circuit (IC) characterization up to 325 GHz.

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Boris Baldischweiler was born in Freiburg, Germany, in 1984. He received the Dipl. Ing. (FH) degree in electrical engineering and M.Sc. degree in microsystems engineering from Hochschule Furtwangen University, Furtwangen, Germany, in 2009 and 2010, respectively. Since 2010, he has been with the Department High Frequency Devices and Circuits, Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg, Germany. His main research concerns noise and cryogenic measurements.

Michael Schlechtweg received the Dipl.-Ing. Degree in electrical engineering from the Technical University Darmstadt, Darmstadt, Germany, in 1982, and the Dr.-Ing. degree from the University of Kassel, Kassel, Germany, in 1989. He then joined the Fraunhofer Institute for Applied Solid State Physics (IAF), Freiburg, Germany, where he has been involved with the design of millimeterwave integrated circuits and nonlinear characterization and modeling of active RF devices. In 1994, he became Head of the Simulation and Modeling Group, Fraunhofer IAF. Since 1996, he has led the RF Devices and Circuits Department, where he has focused on the design and characterization of devices and integrated circuits based on III–V compound semiconductors for RF applications, as well as the development of integrated circuits and modules for sensor and communication systems up to 500 GHz and above. He coauthored approximately 200 scientific publications. He holds two patents. Dr. Schlechtweg was the recipient of the 1993 Fraunhofer Prize and the 1998 European Microwave Prize.

Juan Daniel Gallego-Puyol (M’91) was born in Madrid, Spain, in 1960. He received the Doctor degree in physics in 1992. Since 1985, he has been with the Observatorio Astronómico Nacional (OAN). In 1989, he spent one year with the National Radio Astronomy Observatory. His main research activity has been the development of cryogenic LNAs. He has been involved in numerous international projects in this field. Among others, he has been in charge of the development and construction of cryogenic amplifiers of the Herschel European Space Agency (ESA) mission and of amplifiers for the European contribution to ALMA. Dr. Gallego is a member of URSI and IAU.

Isaac López-Fernández was born in Oviedo, Spain, in 1969. He received the Eng. degree in telecommunication in 1995. In 1994, he joined the Observatorio Astronómico Nacional (OAN), where he was initially involved with the development of receivers for VLBI. In 1995, he was involved with VLBI research with the Harvard Smithsonian Center for Astrophysics. Since 1996, he has focused his research activity on the design and development of cryogenic LNAs within the LNA Laboratory, Observatorio Astronómico Nacional (OAN), where he has carried out designs for European Space Agency (ESA), IRAM, Herschel, and ALMA among others.

Carmen Diez-González was born in Santander, Spain, in 1971. She received the Eng. degree in telecommunication in 1997. From 1998 to 2000, she was involved with the characterization of sub-millimeter wave absorbers and far-infrared p-Ge lasers with SRON and with the Department of Applied Physics, Delft Technical University. From 2000 to 2004, she was with TTI, giving support to the Observatorio Astronómico Nacional (OAN) in the development of IF amplifiers for the European Space Agency (ESA)’s Herschel mission receivers. Since 2004, she has been involved with LNA Laboratory, Observatorio Astronómico Nacional (OAN), where she continues to be involved with Herschel activities, as well as with ALMA and other tasks of the laboratory.

Inmaculada Malo-Gómez was born in Madrid, Spain, in 1972. She received the Eng. degree in telecommunication in 1998 and the Doctor degree in telecommunication in 2011. From 1996 to 2002, she was with telecommunications companies (Telefónica and Orange). In 2003, she joined the Observatorio Astronómico Nacional (OAN). Since then, she has been involved in the development and construction of low-noise cryogenic receivers for Yebes radio telescopes. Her main research interest is in passive and active components for radio astronomy instrumentation.

Enrique Villa was born in Santander, Spain. He received the Telecommunications Engineering degree and Master’s degree in information technologies and mobile networks communications from the University of Cantabria, Santander, Spain, in 2005 and 2008, respectively, and is currently working toward the Ph.D. degree at the University of Cantabria. His research activity is related to the design and perform of radio-astronomy receivers, taking special interest in cryogenic behavior of phase switches, LNAs and detectors, and design, analysis. and testing of microwave devices.

Eduardo Artal received the Engineer and Dr. Engineer in Telecommunication degrees from the Technical University of Catalonia, Barcelona, Spain, in 1976 and 1982, respectively. From 1976 to 1990, he was an Assistant Professor with the Technical University of Catalonia. From 1979 to 1981, while on partial leave from the Technical University of Catalonia, he was with Mier Allende S.A., Barcelona, Spain, where he was involved with TV and FM radio re-emitters development. Since 1990, he has been a Professor with the University of Cantabria, Santander, Spain, where he was Manager of their telecommunication engineering course from 1990 to 1994. From 1994 to 1998, he was Manager of the National Program for Information and Communications Technologies at the “Plan Nacional de I D”, National Research and Development Plan of the Spanish Ministry of Education and Science, Madrid, Spain. His main areas of activities and contributions have been microwave circuits and systems, including monolithic microwave integrated circuits up to 50 GHz. His current research interests are low-noise millimeter-wave amplifiers and receivers for radio-astronomy applications.

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A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN Jing-Hwa Chen, Student Member, IEEE, Sultan R. Helmi, Student Member, IEEE, Hossein Pajouhi, Yukeun Sim, and Saeed Mohammadi, Senior Member, IEEE

Abstract—A wideband radio frequency power amplifier (RF PA) is implemented with a stack of 16 low-breakdown-voltage thin-oxide transistors in a standard 45-nm CMOS SOI technology. A combination of dynamic-biasing and stacking prevents all breakdown mechanisms when the PA operates under large voltage swings and facilitates an output impedance close to 50 without a need for an output-matching network. Using a post-fabrication process, the conductive Si substrate of the CMOS SOI PA is etched away and replaced by a semi-insulating aluminum nitride (AlN) substrate to reduce the effect of substrate parasitic capacitances and improve the PA’s performance. A small-signal gain of 12.2 dB at 1.8 GHz is achieved with a 3-dB bandwidth from 1.5 to 2.6 GHz. For high-reliability operation, the PA is biased with a 15-V power supply and a small transistor current density of 0.2 mA m and delivers a saturated output power of 30.2 dBm and a peak power-added efficiency (PAE) of 23.8%. For a wide range of measured frequencies from 1.5 to 2.4 GHz and under a lower supply voltage of 12 V, and remain above 27.9 and 24.8 dBm, respectively, with peak PAE above 20%. In terms of output power, efficiency, and linearity, the CMOS PA on AlN substrate outperforms its Si counterpart, while both PAs deliver good power performance despite utilizing thin-oxide low-breakdown-voltage transistors. Index Terms—CMOS, radio frequency power amplifier (RF PA), SOI, substrate transfer.

I. INTRODUCTION

W

ITH high operating frequency, relatively low manufacturing cost, and integration capability for radio frequency (RF), digital, and baseband circuits, advanced CMOS technologies are considered the most attractive technology platform for system-on-chip (SoC) radios [1], [2]. Implementing high performance multiband multi-mode linear power amplifiers in advanced CMOS technologies as part of SoC radios, however, remains challenging. The main limitations are: 1) low breakdown voltage of CMOS transistors; 2) high parasitic capacitances of CMOS transistors, passive components, and Manuscript received July 09, 2012; revised September 25, 2012; accepted September 26, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported in part by the U.S. Defense Advanced Research Projects Agency under Grant FA8650-10-1-7053 and by the Purdue University Trask Innovation Fund. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. J.-H. Chen, S. R. Helmi, H. Pajouhi, and S. Mohammadi are with the Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA (e-mail: saeedm@ purdue.edu). J. Sim was with the Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA. He is now with Link-AMedia Devices Corporation, Santa Clara, CA 95051 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2223229

interconnects; and 3) high substrate and conductive losses associated with passive components and interconnects in these technologies. Most CMOS RF power amplifiers (PAs) reported to date have been demonstrated using high-breakdown-voltage CMOS transistors with thick gate oxide and long gate lengths m [3]–[8]. Either power-combining circuits [3], [4] or off-chip matching networks [5]–[7] are used at the output of these PAs in order to reach watt-level performance at RF frequencies. High insertion loss and relatively large parasitics of output matching networks or power combiners generally degrade the performance of CMOS PAs to narrowband and low-linearity characteristics and make them unsuitable for multiband multimode applications. To overcome some of the above limitations, especially transistors’ low-breakdown voltage and to boost the output voltage swing as well as output impedance of CMOS PAs, stacked power PAs have been proposed [5]–[13]. With the exception of our previous work [13], the number of stacked transistors in stacked PAs has been limited to only four transistors. If this number is increased, output voltage swing and output power will further increase. At the same time, by directly matching the stacked PA to a 50- load impedance, output matching network or output power combiners may be eliminated from the PA circuit, and higher efficiencies, higher output powers, and wider bandwidths are achieved. Three simple modifications to previously reported designs help achieve stacked PAs with more than four transistors in the stack, and they are given here. 1) The gate of each transistor in the stack is dynamically biased from the corresponding drain and source terminals such that its voltage follows those of drain and source. 2) Parasitic capacitances to the substrate at all internal nodes are reduced or eliminated. 3) The stack design includes Cascode transistor cells to ensure circuit stability. In this work, a wideband RF PA is implemented using a stack of 16 dynamically biased thin-oxide 1 nm CMOS SOI transistors (eight cascode cells) to achieve a large output voltage swing and an output impedance close to 50 without using any output impedance matching network. The Si substrate is etched away and replaced by a semi-insulating aluminum nitride (AlN) substrate in order to eliminate the adverse effects of parasitic capacitances and further improve the PA performance including its output power, efficiency, and linearity. II. LIMITATIONS IN CMOS PA DESIGN Due to shrinking device dimensions, the safe operating drain–source and drain–gate voltages in CMOS technologies

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Fig. 1. Circuit schematics of PAs designed with: (a) -transistors connected in parallel, (b) power combining of -unit PAs, (c) -common gate transistors in stack, and (d) -common source cells in stack.

have been reduced for each process generation. In order to achieve high linear output power, CMOS PAs have been implemented using large transistors connected in parallel and biased under high current densities, as shown in Fig. 1(a). The low output impedance of such large transistors connected in parallel (typically smaller than a few ) requires an output-matching network with high impedance transformation ratio to match to the 50- load impedance. The high impedance transformation ratio increases the loss contribution of the matching network and significantly reduces the matching bandwidth [14]. Due to thin metal layers and conductive Si substrate, on-chip inductors and transformers in standard CMOS technologies suffer , which makes on-chip matching from low quality factor networks extremely lossy and narrowband. As a result, CMOS PAs based on a parallel combination of transistors and with on-chip matching networks can hardly satisfy the requirements for any of current wireless standards. Another approach to implement RF PAs is to use power combining techniques that combine the output of several unit amplifiers into one single-ended output as shown in Fig. 1(b). Powercombining techniques have been successfully applied to CMOS PAs to achieve high output powers for narrowband applications [3], [4]. The maximum achievable output power and efficiency, however, are limited due to the insertion loss of on-chip power combiners unless very thick nonstandard metallizations are used for their implementation. CMOS PAs designed with stacked thick-oxide transistors, on the other hand, have been proposed to deliver high output power by constructively adding drain–source voltages of individual transistors while providing a high output impedance of close to 50 [5]–[11]. Stacked PAs have been demonstrated using both multiple common gate (CG) cells [6]–[8] and multiple common source (CS) cells with transformer-coupled inputs [9]–[11] as shown in Fig. 1(c) and (d), respectively. Practical implementations of stack transistor PAs have been limited to a maximum of four transistors due to the following limitations. 1) The top transistor in the stack can easily reach gate oxide breakdown for large values of V as its drain voltage

swings between 0 V and 2 V while its gate bias is fixed at a certain voltage. Utilizing thick-oxide transistors with somewhat larger gate-oxide breakdown voltages have only increased the number of stacked transistors to four transistors. 2) A design with -stacked CG transistors is attractive since it achieves an overall voltage swing of times higher than that of a design with -stacked CS transistors. The capacitor loads at the gate terminals of CG transistors form voltage dividers with the gate–drain and gate–source capacitors of transistors in the stack. The values of these gate capacitors must be selected such that the overall voltage swing is distributed evenly across all transistors in the stack. In general, the required gate capacitor at the top of the stack is much smaller compared to the others. As the number of stacked transistors increases, the value of this capacitor decreases rapidly and approaches the parasitic capacitance at the gate terminal for only three to four stacked transistors. 3) In an ideal situation, drain–source voltages of all transistors in an -stacked PA design are identical with no phase difference. The output signal swings between 0 V and a maximum value of , where is the breakdown voltage of a CMOS transistor. Parasitic capacitors among internodal terminals and the common GND break the symmetry of the stacked PA design and force both amplitude and phase variations of drain–source voltages of individual transistors. As an example, simulated time-domain drain–source voltages of a four-stacked CS PA 45 nm, with identical CMOS SOI transistors ( 2 mm) with and without parasitic capacitance to GND (estimated by the post-layout parasitic extractor) are shown in Fig. 2(a) and (b), respectively. When the effect of parasitic capacitors are taken into account [Fig. 2(a)], the top transistor in the stack has a compared substantially higher voltage swing with others and may experience premature breakdown

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Fig. 3. Simplified circuit schematic of the RF CMOS SOI PA designed with eight stacked dynamically biased Cascode cells (16 transistors).

III. STACKED PA DESIGN A. Dynamically Biased SOI Transistors

Fig. 2. Simulated drain–source voltage swings of each transistor in a PA designed with four CS transistors in stack (a) with and (b) without the effect of parasitic capacitances.

before other transistors can contribute significantly to the output voltage swing. Additionally, the variations in the phase caused by these parasitic capacitors reduce the drain–source voltage swing combining efficiency. The overall voltage swing can be expressed by taking the effect of phase variations into account to yield (1) If all transistor cells are conducting with the same phase, a combining efficiency of 100% is achieved. With phase differences among the drain–source voltages of stacked transistors, however, the combining efficiency drops rapidly and limits the power-added efficiency (PAE) [10]. While in principle stacking more transistors should allow a larger voltage swing and thus a larger output power, in practice, variations in the amplitude and phase of drain–source voltages of stacked transistors caused by parasitic capacitors limit the output power and efficiency of stacked PAs with a large number of transistors.

The circuit schematic of the proposed PA is shown in Fig. 3, where 16 electrically isolated thin-oxide 1 nm floating-body CMOS SOI transistors are stacked to increase the total output voltage swing as well as the output impedance. If gate-oxide breakdown does not occur and output voltage signal is distributed evenly among all transistors, it can swing to as high as the sum of the drain–source reach-through voltages of individual transistors . Capacitors and are bypass capacitors. Their values are optimized to achieve high gain and stable operation. In addition to drain–source reach-through voltage, transistors in a stacked PA are also susceptible to gate-oxide breakdown. In the presented PA (see Fig. 3), the gate-oxide breakdown is prevented by a dynamic biasing scheme, as each transistor in the stack is self-biased with a resistor feedback network. Feedback resistors ( – ) set the gate voltage of each transistor within its source and drain voltages , preventing gate-oxide breakdown if the drain–source voltage is limited to values less than reach-through voltage. waveforms of the top Fig. 4 plots the simulated transistor in the stack for input powers of 10, 15, and 20 dBm. Despite the fact that the drain of this transistor swings between 0 V and V , the other terminal voltages swing along with the drain voltage such that neither gate-oxide breakdown nor drain–source reach-through occurs. Other transistors in the stack behave similarly.

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Fig. 4. Simulated voltage swings of the top transistor in the stack of 16 transistors with input powers of 10, 15, and 20 dBm.

The output power of a stacked PA delivered to a 50impedance is expressed according to

load

(2) is the where is the number of transistors in the stack, maximum drain–source voltage across one transistor typically , close to the breakdown voltage of the transistor and is the minimum drain–source voltage of the transistor under its maximum current. For GaAs and GaN power devices is typically 5% to 10% of with high breakdown voltage, the supply voltage. On the contrary, the knee voltage in deepscaled CMOS technology can easily reach 50% of the supply voltage. The high knee voltage reduces the drain–source voltage swing and poses significant limitations on the maximum achievable output power and efficiency. An effective method to reduce the knee voltage is to reduce the current density of the transistor. In the proposed PA design, the stacked transistor configuration allows using high-voltage power supply (15 V) while transis0.2 mA m, tors are biased under a low current density of which suppresses the knee voltage of each transistor for improved power performance and long-term reliability. With the dynamic-biasing scheme, the limiting mechanism in stacking a large number of transistors is the buried oxide (BOX) breakdown ( 80 V in this technology). As the number of stacked transistor increases, however, parasitic capacitance and inductance to the substrate stemming from transistor layout and interconnections and distributed effects of transformers cause significant phase variations across drain–source voltages of individual transistors. This phase imbalance is more significant as the frequency of operation increases and leads to inefficient power combining and hence degradation of output power and PAE. B. Stacked Cascode Cells The CMOS SOI PA is designed using eight stacked Cascode cells as opposed to 16 stacked CS transistors. The overall gain of the presented PA is equal to the gain of a single Cascode cell. Compared with two stacked CS transistors, each Cascode cell offers higher voltage gain, higher output impedance,

Fig. 5. Measured input (red curves) and output (blue curves) reflection coefficients from 1 to 5 GHz of a 2-mm transistor, one Cascode cell implemented with 2-mm transistors, and the PA designed with eight stacked Cascode cells.

better isolation between input and output and hence better stability, and a more compact area since only one transformer is required to drive two transistors. The input RF power is coupled to the PA using on-chip transformers. The primary coils of input transformers are connected in series to increase the overall input impedance. The transformers are designed using the top two copper layers provided in the process with thicknesses of 1.2 m. Using Ansoft High Frequency Structure Simulator (HFSS), we have confirmed that the coupling coefficient of each transformer is above 0.7 in the frequency range of 1–3 GHz. The loss from input transformers degrades the gain of the PA Loss 3 dB but does not affect the maximum output power and efficiency as long as the power gain is not significantly degraded. The distributed effect of the interconnections among stacked cells are modeled as microstrip lines and simulated in Ansoft HFSS. The simulated loss is 0.1 dB/mm at frequencies around 2 GHz. The relatively low loss confirms that the design is not significantly degraded by the interconnections at the operating frequencies of 1.5 to 2.4 GHz. The output impedance of the stacked PA is then calculated as the sum of output impedances of individual cells in the stack as (3) Fig. 5 plots the measured input (red curves) and output (blue curves) reflection coefficients from 1 to 5 GHz of a 2-mm NMOS transistor, one Cascode cell based on two 2-mm NMOS transistors, and the PA designed with eight Cascode cells in the 45-nm CMOS SOI technology. As shown in the figure, by optimizing the size (2 mm) and number of the transistors (eight Cascode cells) in the stacked PA, an output impedance close to 50 over a wide range of frequencies is achieved. Therefore, no output-matching circuit is required, and output

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Fig. 7. Comparison of – characteristics of a 640- m NMOS transistor fabricated in a 45-nm SOI technology before and after post-processing.

Fig. 6. Top: post-processing steps for AlN substrate transfer. Step 1: bonding the chip to a temporary substrate using photoresist. Step 2: etching the backside silicon substrate using XeF . Step 3: releasing the chip from the temporary substrate using acetone. Step 4: bonding the chip to an AlN substrate using a thin adhesive PMMA layer on a heat plate at 80 C. Bottom: die photograph of RF CMOS SOI PA and the chip transferred to AlN substrate.

the SOI flake bonded to AlN substrate. The PA including its pads occupies a chip area of 1.2 mm . IV. MEASUREMENT RESULTS A. Active Device Measurement

power, PAE, and bandwidth degradations caused by lossy on-chip impedance transformation networks are prevented. C. Substrate Transfer Technology The PA is fabricated in a standard CMOS SOI technology with a minimum gate length of 45 nm. In order to demonstrate the importance of eliminating internodal parasitic capacitances to GND in improving the performance, a few samples are postprocessed to remove the Si substrate and replace it with an AlN substrate. The higher thermal conductivity 285 W/m K and slightly lower dielectric constant of AlN substrate compared to silicon ( 145 W/m K, ) combined with its semi-insulating characteristics make it an ideal substrate to implement RF power circuits. By substituting the conductive Si substrate with the semi-insulating AlN substrate, all parasitic capacitances will be in series with very large resistors, effectively eliminating their adverse effects on the PA circuit. The post-processing technology to transfer the device layers of SOI chips to an AlN substrate is shown in Fig. 6, where no photolithography step is necessary. The backside Si substrate is completely etched using Xenon Difluoride XeF silicon dry etching process with an etch rate of 5 m/min at room temperature. The process does not generate plasma, which is a possible cause for transistor performance alteration during etching. The process also has high selectivity between Si and silicon dioxide (1000:1 selectivity); hence, the etching stops at the SOI BOX layer. After the etching, the SOI flake with a thickness of 10 m is bonded at 80 C to an AlN substrate by applying a thin adhesive layer (100 nm) of poly(methyl methacrylate) (PMMA). No air gap between the thin SOI flake and the AlN substrate should be created during the bonding process. Fig. 6 also shows the chip micrograph of the RF CMOS SOI PA and

– characteristics of a 640- m NMOS Fig. 7 shows transistor with a finger width of 0.5 m implemented in the 45-nm CMOS SOI technology before and after substrate transfer. No performance degradation of the active device is observed after substrate transfer to AlN. Small-signal -parameters of the device before and after post-processing technology were also measured, and no degradation in the RF performance was observed. B. Circuit Measurement A major concern in implementing power amplifiers in CMOS SOI technology is the transistor self-heating effect caused by the power dissipated in the transistor and low thermal conductivity of the buried oxide SiO layer. Transistor power gain degrades when it operates at high bias currents and high drain voltages over time. In this particular CMOS SOI technology, the maximum voltage difference permitted across drain–source terminals is about 1.2 V at 105 C. For long-term reliability concerns, a maximum supply voltage of 15 V is selected to ensure that the rms voltages across transistor terminals are within the safe operating range. Additionally, the circuit is designed to operate at low current density of 0.2 mA m to avoid high junction temperature ( 105 C across each transistor. On-wafer small-signal -parameter measurements are performed using a 67-GHz Agilent E8361A network analyzer with short-open-load-thru calibration from 1 to 5 GHz. As shown in Fig. 8, the PA on AlN substrate provides a small-signal power gain of 12.2 dB at 1.8 GHz with 3-dB bandwidth from 1.5 to 2.6 GHz when biased under 12 V 0.15 mA m . The gain is slightly smaller under 9 V 0.1 mA m power supply mainly due to smaller drain current flowing in each transistor (current is set by the self-bias mechanism). The PA is unconditionally stable over the

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Fig. 10. Measured , , and peak PAE of the PA under various supply voltages at 1.8 GHz before and after post-processing. Fig. 8. Measured small-signal -parameters of the stacked PA on AlN substrate under 9- and 12-V supply voltage.

Fig. 11. Measured , , and peak PAE under 12-V supply voltage at various frequencies from 1.5 to 2.4 GHz before and after post-processing.

Fig. 9. Measured , , and PAE versus input power at 1.8 GHz under 15-V supply voltage before and after post-processing.

entire operating frequency as indicated by the stability factor . The large-signal performance is measured using an Agilent E4448A spectrum analyzer with input power provided from an Agilent 83640L CW signal generator and an Agilent 8349B power driver. Fig. 9 compares the power measurement results for CMOS SOI PAs on both Si and AlN substrates. Transferring the substrate to AlN reduces the adverse effects of parasitic capacitance and thus boosts both output power and PAE. The substrate transferred PA delivers a of 30.2 dBm, a of 27.8 dBm and a peak PAE of 23.8% at 1.8 GHz. The effect of varying the supply voltage on the PA performance is shown in Fig. 10, where measured , , and peak PAE of the PA on both Si and AlN substrates at 1.8 GHz are plotted versus supply voltage. By increasing the supply voltage from 9 to 15 V, increases from 25.5 to 30.2 dBm while the peak PAE is between 23.5% and 25.7%. Similar observations are made for the PA on Si substrate with slightly degraded performance compared with the one on AlN substrate. Also note that the bias

current is controlled by the dynamic-biasing scheme which ensures that both linearity and efficiency of the PA do not degrade as the supply voltage varies. The measured , , and PAE versus frequency from 1.5 to 2.6 GHz under 12 V are shown in Fig. 11 for PAs on both Si and AlN substrates. Note that the amplifier demonstrates a wideband power performance as the measured , , and PAE remain constant over the measured frequency range of 1.5–2.4 GHz. The wideband power performance is attributed to the stacked design that achieves matched input and output impedances and high combining efficiency over a wide range of frequencies. For the PA on AlN substrate, and are above 27.9 and 24.8 dBm, respectively, with peak PAE above 20% for the measured frequency range of 1.5–2.4 GHz. Similar observations are made for the amplifier on the Si substrate, with slightly degraded performance attributed to amplitude and phase differences of the drain–source voltages caused by internodal parasitic capacitances. The PA is measured using a wavelength code-division multiple-access (WCDMA) signal with a chip rate of 3.84 Mcps provided by an Agilent E4433B signal generator. The adjacent channel leackage ratio (ACLR) is measured at 5- and 10-MHz offsets from the center frequency. Fig. 12 compares the measured ACLR before and after substrate transfer at the saturated

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TABLE I PERFORMANCE COMPARISON

OF

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CMOS PAS

of 2 to 4 dB is observed compared with the PA on the conductive Si substrate. V. CONCLUSION

Fig. 12. Measured WCDMA output spectra at 1.8 GHz before and after post-processing.

output power for each amplifier. The substrate transfer to AlN technology reduces the effect of parasitic capacitances to GND and thus improves the overall linearity of the PA. For the substrate transferred PA, ACLR of 40.6 and 54.2 dBc are measured at 5- and 10-MHz offset, respectively. An improvement

A fully integrated wideband PA is implemented using dynamically biased stacked Cascode cells in a 45-nm CMOS SOI technology. By optimizing the number and size of transistors in the stack, the output impedance is directly matched to 50 without utilizing an output-matching network. As a result, the PA achieves good power performance and very wide bandwidth suitable for multimode multiband applications. Using a simple post-processing technology, the Si substrate is substituted by an AlN substrate to remove the effects of parasitic capacitances and further improve the PA performance. A watt-level output power with a wide operating bandwidth from 1.5 to 2.4 GHz is achieved despite using low-breakdown thin-oxide CMOS transistors in an advanced technology node. Table I compares the performance of the PA with other reported RF PAs implemented in various CMOS technologies. The implemented PA achieves a large bandwidth and comparable power performance amongst the reported CMOS RF PAs. ACKNOWLEDGMENT The authors would like to thank Dr. S. Raman, Defense Advanced Research Projects Agency, and Dr. R. Worley, Air Force Research Laboratory, for helpful discussions.

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REFERENCES [1] I. Aoki, S. Kee, R. Magoon, R. Aparicio, F. Bohn, J. Zachan, G. Hatcher, D. McClymont, and A. Hajimiri, “A fully-integrated quad-band GSM/GPRS CMOS power amplifier,” IEEE J. Solid-State Circuits, vol. 43, no. 12, pp. 2747–2758, Dec. 2008. [2] B. Ku, S. Baek, and S. Hong, “A wideband transformer-coupled CMOS power amplifier for -band multifunction chips,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 6, pp. 1599–1609, June 2011. [3] I. Aoki, S. D. Kee, D. B. Rutledge, and A. Hajimiri, “Fully integrated CMOS power amplifier design using the distributed active-transformer architecture,” IEEE J. Solid-State Circuits, vol. 37, no. 3, pp. 371–383, Mar. 2002. [4] Y. Tan, H. Xu, M. A. El-tanani, S. Taylor, and H. Lakdawala, “A flipchip-packaged 1.8 V 28 dBm class-AB power amplifier with shielded concentric transformers in 32 nm SoC CMOS,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2011, pp. 426–428. [5] S. Leuschner, J. Mueller, and H. Klar, “A 1.8 GHz wide-band stackedcascode CMOS power amplifier for WCDMA applications in 65 nm standard CMOS,” in IEEE Radio Frequency Integr. Circuits Symp. Dig., Jun. 2011, pp. 1–4. [6] S. Pornpromlikit, J. Jeong, C. D. Presti, A. Scuderi, and P. M. Asbeck, “A watt-level stacked-FET linear power amplifier in silicon-on-insulator CMOS,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 1, pp. 57–64, Jan. 2010. [7] M. Fathi, D. K. Su, and B. A. Wooley, “A stacked 6.5-GHz 29.6-dBm power amplifier in standard 65-nm CMOS,” in Proc. IEEE Custom Integr. Circuits Conf., Sep. 2010, pp. 1–4. [8] J. Jeong, S. Pornpromlikit, P. M. Asbeck, and D. Kelly, “A 20 dBm linear RF power amplifier using stacked silicon-on-sapphire MOSFETs,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 12, pp. 684–686, Dec. 2006. [9] J. G. McRory, G. G. Rabjohn, and R. H. Johnston, “Transformer coupled stacked FET power amplifiers,” IEEE J. Solid-State Circuits, vol. 34, no. 2, pp. 157–161, Feb. 1999. [10] M. Lei, Z. Tsai, K. Lin, and H. Wang, “Design and analysis of stacked power amplifier in series-input and series-output configuration,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2802–2812, Dec. 2007. [11] P. Huang, Z. Tsai, K. Lin, and H. Wang, “A high-efficiency, broadband CMOS power amplifier for cognitive radio applications,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 12, pp. 3556–3565, Dec. 2010. [12] J. Chen, S. R. Helmi, and S. Mohammadi, “Millimeter-wave power amplifiers in 45 nm CMOS SOI technology,” in Proc. IEEE Int. SOI Conf., Oct. 2011, pp. 1–2. [13] J. Chen, S. R. Helmi, H. Pajouhi, Y. Sim, and S. Mohammadi, “A 1.8 GHz stacked power amplifier in 45 nm CMOS SOI technology with substrate-transferred to AlN,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [14] T. H. Lee, The Design of CMOS Radio Frequency Integrated Circuits. Cambridge, U. K.: Cambridge Univ. Press, 1998. [15] B. Jin, J. Moon, C. Zhao, and B. Kim, “A 30.8-dBm wideband CMOS power amplifier with minimized supply fluctuation,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 6, pp. 1658–1666, Jun. 2012. [16] B. Francois and P. Reynaert, “A fully integrated watt-level linear 900-MHz CMOS RF power amplifier for LTE-applications,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 6, pp. 1878–1885, Jun. 2012. [17] A. F. Aref and R. Negra, “A fully integrated adaptive multiband multimode switching-mode CMOS power amplifier,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 8, pp. 2549–2561, Aug. 2012.

Jing-Hwa Chen (S’10) received the B.S. degree in electrical engineering from National Central University, Jhongli, Taiwan, in 2007. He is currently working toward the Ph.D. degree in electrical and computer engineering at Purdue University, West Lafayette, IN. During fall 2012, he was an Intern Engineer with Peregrine Semiconductor. His research interests include analog and RF circuit design and microwave and millimeter-wave CMOS power amplifier design.

Sultan R. Helmi (S’11) was born in Jeddah, Saudi Arabia, in 1982. He received the B.S. degree from King AbdulAziz University, Jeddah, Saudi Arabia, in 2005, and the M.S. degree from Purdue University, West Lafayette, IN, in 2011, where he is currently working toward the Ph.D. degree, all in electrical and computer engineering. His research interests include the design of power amplifiers, RF circuits, and RF components using CMOS technology.

Hossein Pajouhi received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 2008. He is currently working toward the Ph.D. in electrical engineering at Purdue University, West Lafayette, IN. His research interests focus on nano-electromechanical systems.

Yukeun Sim received the B.S. and M.S. degrees in electrical engineering from Purdue University, West Lafayette, IN, in 2008 and 2010, respectively. During his graduate studies, he was engaged in the research of RF front-end architecture, low-noise amplifiers, and power amplifiers. In 2010, he joined Link-A-Media Devices, in Santa Clara, CA. as a Senior Design Engineer. Since then, he has been involved in the design of high-speed phase-locked loops for storage applications, such as SSD, HDD, and hybrid.

Saeed Mohammadi (S’89–M’92–SM’02) received the Ph.D. degree in electrical engineering from the University of Michigan, Ann Arbor, in 2000. He is currently an Associate Professor of electrical and computer engineering with Purdue University, West Lafayette, IN. His research interests include RF devices and circuits and nanotechnology.

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PA Efficiency and Linearity Enhancement Using External Harmonic Injection Asmita Dani, Student Member, IEEE, Michael Roberg, Student Member, IEEE, and Zoya Popović, Fellow, IEEE

Abstract—This paper presents analysis and experimental demonstration of a high-efficiency linear power amplifier (PA) with second-harmonic injection at the output. In this circuit, the transistor is not driven hard into compression and does not produce significant harmonic content. External injection at the output enables voltage and current wave-shaping to achieve high efficiency. Theoretical analysis of the waveforms shows that the maximal drain efficiency is 89.9% with, at most, 0.13 dB of reduction in output power compared with the class-A case. The overall PA efficiency is derived in terms of the injector circuit efficiency. A harmonically injected prototype GaN HEMT 2.45-GHz PA demonstrates over 80% efficiency with linearity improved over the class-AB PA without harmonic injection. Two-tone measurements show a reduction of the third-order intermodulation by 30 dBc in the linear region and greater than 10 dBc in saturation. Index Terms—Amplifier drain efficiency, Fourier coefficients, harmonics, linearity, microwave power amplifiers (PAs), third-order intercept, waveform shaping.

I. INTRODUCTION

A

large portion of current research in high-power amplification of signals with carriers in the microwave range focuses on improving efficiency and linearity. There are many power amplifier (PA) topologies that achieve high efficiency by driving the active device into a nonlinear region and shaping voltage and current waveforms across the device via proper selection of the output loading network at harmonic frequencies. These techniques, such as class-F and PA topologies, rely on the nonlinear active device for harmonic current or voltage generation [1]–[4]. The concept of harmonic injection, however, refers to architectures in which power at one or more harmonics of the operating frequency is supplied externally to either the input, output, or both input and output of the active device. Analysis of efficiency improvement of tube PAs using harmonic injection into both the grid (input) and plate (output) has been presented in [5]–[7]. A harmonic-injection scheme referred to as a harmonic reaction amplifier was presented in [8]. The harmonic reaction amplifier uses two parallel devices Manuscript received July 09, 2012; revised September 19, 2012; accepted September 20, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported in part by the Berrie Hill research Corporation and the U.S. Air Force under Contract FA8650-10-D1746-0006. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. A. Dani and Z. Popović are with the Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, CO 80309-0425 USA (e-mail: [email protected]; [email protected]). M. Roberg is with TriQuint Semiconductor, Richardson TX 75080 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222918

Fig. 1. Block diagram of a harmonic-injection PA (HI-PA) with second-harmonic injection at the output. A three-port network at the output allows isolaand between ports 2 and 3, while allowing low tion between waves at between ports 1 and 2. The phase of the injected harmonic is critical loss at to obtaining high efficiency.

and effectively acts as a push–pull amplifier with respect to the second harmonic. In 1992, a patent was issued for a harmonic injection amplifier in which the harmonic signal created using a frequency multiplier is injected into the transistor output [9]. A class-E VHF PA at 3.5 MHz with a secondary class-E 7-MHz PA injector is presented in [10]. An experiment demonstrating 15.2% efficiency improvement of a 2-GHz GaN PA using second-harmonic injection at the input is reported in [11]. More recently, a concept for efficiency improvement via injection of harmonics into the output of a class-B/J amplifier was demonstrated [12]. A novel scheme of efficiency improvement of a class-E amplifier using input harmonic injection via a feedback loop was shown in [13]. In this paper, we discuss injection of power at the second harmonic, as shown in the block diagram of Fig. 1 and the implications on efficiency and linearity. The approach is valid for any amplifier mode, not just for class-B/J as in [12] and [14]. The contributions of this work are organized as follows. • Section II presents, for the first time, a theoretical Fourierexpansion analysis of output harmonic injection. A relationship between the total efficiency and injected power is presented for the case of second-harmonic injection. The analysis gives an insight into the impedance that needs to be synthesized at the output of the transistor at the fundamental and harmonic frequencies. The effect of efficiency of the injector circuit on the total efficiency is calculated. • Section III discusses two prototypes used for experimental validation, one based on a packaged Cree GaN 10-W 50class-AB PA and the other based on a TriQuint GaN die with an injection network designed for a non-50- environment. • Section IV presents measurement results for the relevant amplifier parameters as a function of the phase and amplitude of the injected harmonic signal for both prototypes.

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The experimental results demonstrate an improvement from 58% to 80% in efficiency with an output power of 37 dBm and over 20-dB gain from a single TriQuint 6-W device. In addition, the amplifier linearity is shown to be improved with harmonic injection w.r.t. the class-AB case, which implies significant linearity improvement compared with the same device used in harmonically terminated compressed nonlinear PAs. II. THEORETICAL ANALYSIS The theoretical analysis of a harmonically injected PA (HI-PA) shown in Fig. 1 is developed based on Fourier expansions of the voltage and current waveforms at the current source of the transistor, expanding on the approach in [12] and [15]. First, expressions are derived for injected voltage which optimizes efficiency, followed by the analysis of total dissipated power and a discussion of linearity. To obtain an HI-PA, a linear three-port network is cascaded at the output of a linear PA, and the required -parameters of that network are given in [15].

Fig. 2. Optimal drain current and voltage waveforms for second-harmonic injection amplifier, normalized to 1-W output power.

where corresponds to a point at which the first derivative of the voltage waveform w.r.t. is equal to zero. Note that (5) is only valid when (7)

A. Waveform Analysis Consider the normalized drain voltage and current waveforms at the virtual drain of a linear field-effect transistor (FET) PA, which are given by (1) (2) where , and the bar indicates a normalized quantity. For instance, when , the normalized class-A output power is 1 W, and the waveforms result in 50% efficiency. If the drain waveforms can be shaped by harmonic content in a manner such that the overlap of the voltage and current is minimized for a given fundamental frequency output power, then drain efficiency will be maximized. Consider the addition of only the second-harmonic term in (1) and (2). In order to maintain waveform symmetry, only cosinusoidal components are added. Such a condition will result in the voltage waveform of the same shape but 180 out of phase with the current waveform. The waveforms following addition of a second-harmonic term become

Therefore, the range of

over which (5) is valid is limited to (8)

It remains to be proven which critical points correspond to the global minima and global maxima. Substituting the critical point in (5) into the second partial derivative of (3) results in (9) If is negative in sign, the critical point corresponds to a minimum, while, if it is positive in sign, then it corresponds to a maximum. Applying the second derivative test to the critical point described by (6) results in (10) Therefore, the critical point described by (6) will be an extremum as follows: is a minimum

(11)

is a maximum

(12)

(3) (4) as shown in Fig. 2, showing minimal overlap of the voltage and current waveforms. From (3) and (4), it can be concluded that the impedance at is the negative of that at . Effectively, this requires that power is delivered to the transistor at the second harmonic. An optimal value of that maximizes the efficiency can be found. First, the critical points of the drain current and voltage waveforms are expressed as (5) (6)

B. Efficiency Analysis The normalized total DC power consumed by the amplifier is expressed as (13) is the efficiency of the injector circuit. Note that, due where to the symmetry of the current and voltage waveforms, , the optimal dc supply voltage is that which results in a drain voltage waveform with minimum of zero. Therefore, from (3), we have (14)

DANI et al.: PA EFFICIENCY AND LINEARITY ENHANCEMENT USING EXTERNAL HARMONIC INJECTION

Fig. 3. Contour plot for .

as a function of

and injector circuit efficiency

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Fig. 4. Optimal solution for Fourier coefficient and second-harmonic delivered power relative to fundamental frequency output power versus second . harmonic injector circuit efficiency

The total dc power may now be expanded to the form

(15) (16) Since we use a normalization that sets the fundamental output power to 1 W, the total efficiency is calculated as the inverse of the normalized dc power

Fig. 5. Total efficiency

versus injector circuit efficiency

.

(17)

power , also shown in Fig. 4. The PA efficiency is determined by inserting into (15) and (16) to yield

Fig. 3 shows the total efficiency plotted as a function of both and normalized magnitude of secondinjector efficiency . harmonic The value of is optimized by setting the partial derivative of w.r.t. the Fourier coefficient to zero and solving for as follows:

(20)

(21) (18) (22) (19) , the optimal These values minimize . Given . A plot of , Fourier coefficient reduces to which corresponds to the amplitude of the required injected second-harmonic versus , is shown in Fig. 4. As one would expect, the magnitude of the Fourier coefficient decreases as the injector efficiency decreases. Another interesting parameter to investigate is the ratio of the delivered fundamental output power to the required delivered second-harmonic injected

(23) A plot of the total efficiency versus injector circuit efficiency is shown in Fig. 5 for optimized solution at and a plot for as a function of , and is shown in the total efficiency Fig. 3. The maximum value is 89.9%, and it rolls off reasonably slowly with decreasing injector efficiency. This is intuitive because the power required from the injector is significantly lower

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relative to 1 W. When , the output power is only reduced by only 0.13 dB relative to the class-A amplifier. Also, it is of practical interest to find the supply voltage and current normalized to class-A: (30)

Fig. 6. Power reduction and normalized supply voltage relative to class-A versus injector efficiency .

than the fundamental output power of the amplifier, as shown in Fig. 4. As expected, when the amplifier efficiency reaches 50%, the injector circuit is turned off. In this case, the amplifier degenerates to the canonical class-A mode. As previously mentioned, the load presented to the transistor at the second harmonic is the negative of that presented at the fundamental, so the load resistance normalized to the class-A fundamental load is 1. To find the output power of the PA normalized to class-A output power, normalization conditions corresponding to peak voltage and current constraints are enforced. and are now found, enabling determination of the maximum instantaneous normalized voltage and cur, and the output power normalized to the class-A amrent plifier output power is determined. The normalized dc voltage is expressed as

(24) (25) Note that, due to the symmetry of the current and voltage wave, the maximum normalized voltage is calcuforms lated as (26) (27) The output power normalized to class-A is then given by (28)

(29) Fig. 6 depicts the fundamental frequency output power reduction relative to a class-A amplifier versus the injector efficiency. This was calculated by computing as a function of , then and determining the ratio computing the output power from

Fig. 6 shows the normalized supply voltage which is approxi. mately 0.7107 for A similar analysis can be performed for third-harmonic injection at the output, since symmetric square waveforms can be achieved using odd harmonics only. In the case of third-harmonic injection, the impedance at the third harmonic is positive rather than negative, so the ideal waveforms can be realized with a passive set of output terminations. The analysis shows, however, that the total efficiency given by (22) and (23) is around 65% for injector efficiencies above 40% and does not reach the high efficiencies of the second-harmonic injection case. Details of the analysis can be found in [16]. C. Linearity Transistors exhibit nonlinearities due to various factors such as input and output device capacitance, transconductance, and drain–source resistance resulting in a characteristic between and , which can be represented using the power series

(31) where . As seen in (31), the second-order nonlinearity causes an additional dc component and a signal at twice the fundamental frequency to appear in the output voltage. For a two-tone signal, the second-order nonlinearity can be easily filtered out and does not cause any in-band distortion of the signal. However, the third-order nonlinearity results in in-band distortion products. The gain of the fundamental component under nonlinear operation can be expressed in terms of the fundamental gain and the third-order gain and amplitude, and the derivation is given in [17]. The analysis in [17] also shows that the amplitude of the second-harmonic output signal is inversely proportional to the magnitude of the transfer characteristic of the amplifier at the third harmonic, which is referred to in Section IV. A good discussion on extracting linearity information from a continuous-wave (CW)-fed amplifier by measuring the third-harmonic output content is presented in [18]. Based on this theory, in this paper, a CW signal is used for harmonic injection analysis as the device enters saturation. In particular, we measure second and third harmonic as a function of the injected power and phase in order to assess the linearity. III. PROTOTYPE PA DESIGN Two prototype PAs were used to demonstrate the HI-PA concept. A packaged device in a demo board with class-AB broadband PA configuration is injected through a 50- three-port injection circuit described in more detail in [12], [14], and [15]. In order to have more design freedom and lower matching network loss, a TriQuint GaN die was used in the second narrowband prototype with a non-50- three-port injector circuit.

DANI et al.: PA EFFICIENCY AND LINEARITY ENHANCEMENT USING EXTERNAL HARMONIC INJECTION

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Fig. 8. Measured drain efficiency at PA shown in Fig. 7 without injection.

and

and gain for the class-AB

Fig. 7. Hybrid HI-PA with a 6-W TriQuint TGF2023-01 die. The output at network integrates the harmonic injection three-port network with matched to 65 and at matched to 71 . The input network does an impedance transformation from 50 to 10 in order to achieve high gain and at the fundamental.

A. Packaged Device Prototype PA is used in a broadA Cree GaN HEMT with 10-W band (DC-6 GHz) demo board provided by the manufacturer (CGH40006P-TB) with a packaged device and matched to 50 as the first prototype. This PA gives 40 dBm at 2.45 GHz with and 12 dBm [15]. The input power to the fundamental PA is swept from 22 to 34 dBm (linear to saturation) with the drain bias at 22 and 28 V. The gate bias was set to 1.6, 1.8, and 2 V for a class AB mode. The fundamental PA starts compressing at an input power level of 27 dBm when no harmonic injection is present. B. Discrete Die Prototype PA A hybrid class-AB PA is designed using load-pull measurements on the TriQuint TGF2023-01 device at 2.45 GHz, as shown in Fig. 7. The reference plane for all measurements on this PA is the virtual drain of the transistor, i.e., the current source behind the output capacitance of the device. The HI-PA is designed with the three-port injection network integrated into the output matching circuit of the amplifier in order to minimize loss. Design and performance of the injection network is similar to the one presented in [12] and [15] with the fundamental and second-harmonic impedances matched close to 65 as explained in (3) and (4). Due to fabrication tolerances, the fundamental impedance at the virtual drain of the device was found to be matched to 65 and the impedance to 71 (10% higher). This class-AB PA has 58% drain efficiency with an output power of 37 dBm without any harmonic injection at a drain bias voltage of 28 V. Fig. 8 shows the measured drain efficiency , output power at fundamental , third harmonic , and the gain as a function of fundamental . input drive power IV. HI-PA MEASUREMENTS AND ANALYSIS The block diagram shown in Fig. 9 shows the measurement setup for HI-PA prototypes. A portion of the fundamental input is frequency doubled to create the second harmonic for injection. A voltage-controlled phase shifter and variable gain

Fig. 9. Block diagram of the HI-PA measurement setup. The input signal is split . A voltage and frequency doubled to create the injected harmonic, controlled phase shifter and variable gain amplifier are used to control the am. plitude and phase of

amplifier (VGA) are used to control the amplitude and phase at . All of the measurements are de-embedded to the virtual drain of the transistor by calibrating the loss in the output network and taking into account the intrinsic transistor parasitics, i.e., output capacitance of the device. A bondwire model in Ansoft High Frequency Structure Simulator (HFSS) was simulated to consider the inductance loss in the bondwire transition for the hybrid PA design. The drain efficiency for an HI-PA takes into account the amount of second-harmonic power injected into the virtual drain of the device assuming as follows: (32) where

.

A. Packaged Device Prototype HI-PA Fig. 10 compares the measured efficiency, output power, and gain for the PA with and without harmonic injection. It is seen that the HI-PA saturates at a higher input power (32 dBm) as compared with the class-AB PA (27 dBm), resulting in higher

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Fig. 11. Comparison of power levels for single-tone and third-order IMD products for HI-PA and class-AB PA without harmonic injection.

phase adjustment. The measured results in Fig. 10 show that the HI-PA (marked line) saturates at a higher input power than the PA with no harmonic injection (solid line). At lower input powers, the IMD3 level is over 30 dB lower for the HI-PA and remains 10 dB lower after the PA saturates. In Fig. 11, only the frequency is injected, resulting in a decrease in the IMD while the remains unchanged. Symmetrically, is injected, the will decrease. Both of the when IMD products will be reduced equally for a signal injected at . This is consistent with measurements obtained with tube amplifiers in [19] and harmonic injection at input of solid-state amplifiers in [20], [21]. B. Discrete Die Prototype HI-PA

Fig. 10. Comparison of measured (a) drain efficiency, (b) , and (c) 22 V, 28 V gain for the HI-PA to the PA with no harmonic injection at 1.6 V (class-AB). The dashed green line indicates input power at and which the PA becomes nonlinear.

linearity. The gain of the HI-PA is lower by about 1 dB as compared with the fundamental PA in the linear region, but remains higher in saturation. Harmonic balance simulations using a nonlinear model provided by the manufacturer show the same trends for gain as the measured data. Measured results show that higher efficiency can be achieved for a constant output power with HI-PA by changing the operating bias point. For instance, the drain efficiency of the PA improves from 58% with no injection to 75% with injection for an output power of 40 dBm by changing the drain bias from 28 to 22 V. A two-tone linearity test is performed at 22 V 1.8 V. The two tones are kept 5 MHz apart and with 2.45 GHz and third-order intermodulation (IMD3) products generated at 2.455 GHz 2.46 GHz. Simultaneously, , , or and is injected at the output, each requiring a different

The HI-PA using a TriQuint 6-W GaN discrete high-electron mobility transistor (HEMT) in a class-AB PA achieves a high total drain efficiency of 89% with external second-harmonic injection at the output at a bias voltage of 22 V. This efficiency is very close to the theoretical efficiency of 89.9% from Fig. 3, though one would expect it to be lower. The reason being that the theory is derived for an ideal device with ideal – curves which do not take into account knee voltage of the transistor and does not generate any odd-order harmonics. In practice, the PA always generates some harmonic content even at lower input power levels. The gain of the amplifier reduces by 1 dB as compared with the amplifier without any harmonic injection. Fig. 12 shows a comparison of the measured performance for the HI-PA and PA without harmonic injection. These measurements are optimized for high efficiency and hence the amplifier is nonlinear at . It is seen that a better performance is achieved with the discrete device as compared with the results presented in Fig. 10 for the packaged device, as expected. As seen in the theoretical analysis (30), harmonic injection implies a shift in the bias voltage in order to get the optimum performance from the amplifier. Fig. 13 shows the performance of the HI-PA at different drain bias voltages for a fundamental input drive of 16.2 dBm. The HI-PA is then optimized in order to get high efficiency along with linearity. As explained in Section II-C, for a CW amplifier, the values of can give an estimate of the linearity. It is seen 24 V, the drain efficiency of the from Fig. 13 that, at HI-PA is improved by over 20% as compared with the class-AB

DANI et al.: PA EFFICIENCY AND LINEARITY ENHANCEMENT USING EXTERNAL HARMONIC INJECTION

Fig. 14. Contour plots of (a) measured fundamental output power . dBm and (b) drain efficiency

Fig. 12. Comparison of measured (a) , (b) , and (c) gain for discrete die prototype of HI-PA optimized for maximum efficiency.

Fig. 13. Drain efficiency with the ratio

, 0.1 and

for different bias voltages 16.2 dBm.

PA with no injection, and the output power at the third harmonic is lowered by 30 dB for an input drive level of 16.2 dBm. At this bias point, conditions for high linearity

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in

and high drain efficiency are obtained with a nominal fundareduction of 0.26 dB over the mental output power PA without any injection. Note that, when harmonic injection is performed, it results in higher fundamental output power due to reduction in other harmonic content. In order to keep the output power constant and reduce the dc power dissipation, the drain supply voltage can be reduced to a certain extent, as shown in Fig. 13. The supply voltage reduction is only advantageous up to a device-dependent lower value when the output power starts decreasing. In the case of packaged prototype, 22 V was found to be optimal, and, in the case of discrete prototype, this value was 24 V. Note that the PA with no injection is not designed for high efficiency, since it is biased in class-AB, and the gate bias is kept the same for the PA with and without injection. All of the measurements presented in the remainder of the paper will be at 24 V. As discussed in Section II-A, the injected second-harmonic signal needs to be at a particular phase and amplitude in order to shape the voltage and current waveforms at the virtual drain of the amplifier. If the input drive is kept constant, various parameters affecting the performance of the HI-PA such as , drain efficiency , drain current , and power at the vary with the amplitude and harmonics phase of injected second harmonic power as shown in Figs. 14 and 15. Figs. 14 and 15 show that, for 9 dBc and a phase shift of 80 , high drain efficiency of 79% is achieved using (32) along with extremely low values of . Note that this efficiency takes into account the power of the injected

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Fig. 16. Comparison of drain efficiency and gain for HI and PA with no injec. tion as a function of

Fig. 15. (a) Drain current (amperes) and (b) third-harmonic output power in dBm for 16.2 dBm depicting the variation in the values of these parameters as a function of phase and power level (dBc w.r.t. ) of the injected second harmonic . Analogous plots can be . obtained for the second-harmonic output power

signal. However, the efficiency of the injector circuit is not included in this proof-of-concept experiment in which the HI-PA is not fully integrated. The value of obtained at this point is approximately 37 dBm, which is only 0.2 dB lower than the fundamental output power obtained with no injection (Fig. 8). The measurements show that, if is not at the optimum phase and amplitude, the performance of the amplifier can severely degrade. When the second-harmonic voltage is out of phase relative to the optimal value, the amplitude of increases, making the amplifier extremely nonlinear. The efficiency reduces from 80% to 40% while the output power drops more than 3 dB. If is higher than the optimum value (in this case, 9 dBc), then, even at the optimum phase of the injected harmonic, the HI-PA is highly nonlinear. This is due to undesired additional second-harmonic content in the output voltage and current waveforms generated by the device under hard drive. A sweep is performed at in order to achieve the optimal performance of the HI-PA at various input drive levels. Since an amplifier undergoes AM–AM and AM–PM distortion, the optimal phase and amplitude of the injected second-harmonic changes for different input drive levels. Fig. 16 shows a comparison of the gain and drain efficiency obtained for HI-PA and PA without harmonic injection as a function of . The efficiency obtained at each input drive level is for an optimal value of amplitude and phase which are also dependent on

Fig. 17. Comparison of and as a function of for HI and PA with no injection. The graph also shows the amplitude of as a function of in order to achieve high efficiency and linearity performance for the HI-PA.

. The overall gain of the HI-PA is reduced by 1 dB, and the 1-dB compression point of the HI-PA is shifted to a higher of 15.7 dBm, implying improved linearity. The drain efficiency improvement ranges from 8% to 20% as the input drive level increases. The comparison of and for the HI-PA and as PA with no injection is shown in Fig. 17 along with a function of . As derived in [17], the transconductance at the third harmonic is inversely proportional to the amplitude of the second harmonic. The value for gain of an amplifier under nonlinear operation can be given from (31) as (33) where and are values for transconductance at fundamental and third harmonic. Therefore, it is seen that the value of required to lower the value of for the HI-PA is exactly equal to . The nominal class-A operation of the PA without harmonic injection with a 50% drain efficiency is achieved at 13 dBm. Fig. 17 shows that, at this input drive level, the amplitude of required in order to achieve an optimum performance in terms of efficiency and linearity for the HI-PA is 10 dBc. This result matches with the theoretical analysis presented in Fig. 4 where, for a 100% injector efficiency, the ratio of to is 0.1 for a class-A bias point.

DANI et al.: PA EFFICIENCY AND LINEARITY ENHANCEMENT USING EXTERNAL HARMONIC INJECTION

Fig. 18. Comparison of power at , for HI-PA and PA without harmonic injection as a function of input drive level. to The graph also shows the power injected at the second harmonic tone . achieve lowest

Two-tone measurements with optimization for the amplitude and phase of the injected second harmonic in order to achieve lowest IMD3 products in both lower and upper sidebands are performed. This measurement is similar to the one presented in Section IV-A for the packaged device prototype HI-PA where either or are injected at the output of the HI-PA. Here, the injection of affects the perat and at due to formance of active impedance synthesis at the injection port. It is important to note that the reduction in results from mixing of and distortion products caused due to second-order nonlinearities. It is seen that the reduction in using external second-harmonic injection is greater than 15 dB for different input drive levels, whereas at and at remain unaffected. Fig. 18 shows the reduction in power levels for and achieved for different fundamental input drive levels along with the amount of injected power. For practical communication signals, the harmonic injection path needs to be modified in order to inject an exactly doubled spectrum of the signal. As seen in the two-tone measurements, injection at one harmonic tone only affects the distortion products which are a function of that harmonic tone frequency. Since, a modulated signal in general is a multitone signal, it will require a injected signal with twice the modulation bandwidth and RF carrier. This can be accomplished by baseband signal up-conversion. V. DISCUSSION The results above show that a PA with harmonic injection in the output can be both efficient and linear. In the demonstrated results above, we start with a class-AB PA, which is not perfectly linear. In fact, the theory shown in Section II assumes that some second-harmonic content is generated by the active device. If the transistor fails to generate second-harmonic power and presents an impedance other than that of the fundamental frequency output termination, the necessary negative impedance cannot be synthesized using harmonic injection. In this case, harmonic injection at both the input and output of the transistor would be required.

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Fig. 19. Minimum and measured at virtual drain of the 16.2 dBm. The minimum for is obtained with HI-PA for 17.8 dBc w.r.t. , whereas minimum for is 8.9 dBc. obtained for

It is of interest to discuss some limitations on linearity and efficiency that are practically achievable. We have shown that the third harmonic, which directly affects IMD performance, is minimized for a specific phase and amplitude of the injected second harmonic. However, the injected signal also affects the nonlinear content in the waveform produced by the transistor, which can be evaluated by measuring the level of the second harmonic at the output. The amount of injected second-harmonic power that results in a minimum of harmonic content in the output is shown in Fig. 19. Note that the second and third harmonic have minima for different injected power levels of the second harmonic. The amplitude of needed to lower is approximately 10 dB less than that needed to lower . Also, the phase shift for injection differs by 50 . As seen from Fig. 14, the drain efficiency drops by approximately 10% between these two points in amplitude and phase. For a modulated input signal, the third-order nonlinearities have to be minimized since they create in-band distortion which is extremely difficult to filter. The third-order distortion products are a function of the amplitude of second harmonic produced by the amplifier itself. Hence, a point in the amplitude and phase of the injected signal needs to be chosen to optimize linearity by a tradeoff between the second- and third-harmonic content. The main practical limitation on efficiency is the implementation of an efficient injector circuit. Fig. 5 shows that an injector efficiency of 40% or higher, with a power level 10 dB below the output power, is required to obtain an overall efficiency above 80%. This might present a challenge for very high-power PAs, but is otherwise not a difficult constraint. In the prototype characterization presented in this paper, a passive doubler was used to produce the harmonic. This is not only inefficient but also impractical for amplifying a real signal, in which case significant distortion would be introduced. The linearity tests (Fig. 11) show that a clean doubled frequency spectrum needs to be injected. Therefore, for signal amplification, a different approach is needed than was done for the CW tests in this paper. A topic of current research is integration of an up-converter in the injection circuit with a synchronized second baseband input. For very broadband signals, the phase control that achieves linearity might prove to be challenging. An interesting extension of the concept to a broadband HI-PA

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will require a three-port injection network design with good harmonic isolation and low fundamental frequency loss over a broad frequency range. In summary, this paper presents a theoretical Fourier analysis of PAs with harmonic injection at the output, showing limits on total circuit efficiency. The theory is experimentally verified on class-AB 2.45-GHz PAs using both packaged and discrete GaN HEMTs, resulting in 75% and 80% efficiencies, respectively, at the 1-dB compression points. The linearity of the PA is shown to be significantly improved for specific phase and amplitude of injected second harmonic, with simultaneous improvement in efficiency. To the best of our knowledge, these are the first reported efficient linear PAs of this type using solid-state devices. REFERENCES [1] F. Raab, “Class-E, class-C, and class-F power amplifiers based upon a finite number of harmonics,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 8, pp. 1462–1468, Aug. 2001. [2] F. Raab et al., “Power amplifiers and transmitters for RF and microwave,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 814–826, Mar. 2002. [3] S. Kee, I. Aoki, A. Hajimiri, and D. Rutledge, “The class-e/f family of zvs switching amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 6, pp. 1677–1690, Jun. 2003. [4] M. Roberg and Z. Popovic, “Analysis of high-efficiency power amplifiers with arbitrary output harmonic terminations,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 8, pp. 2037–2048, Aug. 2011. [5] Z. Zivkovic and A. Markovic, “Increasing the efficiency of the high-power triode HF amplifier—Why not with the second harmonic?,” IEEE Trans. Broadcasting, vol. BC-32, no. 1, pp. 5–10, Mar. 1986. [6] Z. Zivkovic-Dzunja and A. Markovic, “Plate and grid modulated HF high-power tuned amplifier with increased efficiency,” IEEE Trans. Broadcasting, vol. 35, no. 1, pp. 97–107, Mar. 1989. [7] A. Juhas, L. Novak, and S. Kostic, “Signals with flattened extrema in balance power analysis of HFHPTA: Theory and applications,” IEEE Trans. Broadcasting, vol. 47, no. 1, pp. 38–45, Mar. 2001. [8] S. Nishiki and T. Nojima, “Harmonic reaction amplifier—A novel high-efficiency and high-power microwave amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., 1987, pp. 963–966. [9] D. Willems, E. L. Griffin, I. J. Bahl, and M. D. Pollman, “High Efficiency Harmonic Injection Power Amplifier,” U.S. Patent 5 172 072, Dec. 15, 1991. [10] A. Telegdy, B. Molnar, and N. Sokal, “Class-em switching-mode tuned power amplifier-high efficiency with slow-switching transistor,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 6, pp. 1662–1676, Jun. 2003. [11] H. Matsubara, F. Kawanabe, and T. Nojima, “A 2-GHz band experiment on efficiency enhancement of a GaN power amplifier using 2nd harmonic injection,” in Proc. Asia–Pacific Microw. Conf., 2008, pp. 1–4. [12] A. AlMuhaisen, P. Wright, J. Lees, P. Tasker, S. Cripps, and J. Benedikt, “Novel wide band high-efficiency active harmonic injection power amplifier concept,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2010, pp. 664–667. [13] H. R. Bae, C. S. Cho, and J. W. Lee, “Efficiency enhanced class-E power amplifier using the second harmonic injection at the feedback loop,” in Proc. Eur. Microw. Conf., 2010, pp. 1042–1045. [14] A. AlMuhaisen, P. Wright, J. Lees, P. Tasker, S. Cripps, and J. Benedikt, “Wide band high-efficiency power amplifier design,” in Proc. Eur. Microw. Integr. Circuits Conf., Oct. 2011, pp. 184–187. [15] A. Dani, M. Roberg, and Z. Popovic, “Efficiency and linearity of power amplifiers with external harmonic injection,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [16] M. Roberg, “Analysis and design of non-linear amplifiers for efficient microwave transmitters,” Ph.D. dissertation, Dept. Electr., Comput. Energy Eng., Univ. Colorado, Boulder, 2012. [17] I. J. Bahl, Fundamental of RF and Microwave Transistor Amplifiers. Hoboken, NJ: Wiley, 2009, ch. 12, pp. 332–333.

[18] P. B. Kenington, High-Linearity RF Amplifier Design. Norwood, MA: Artech House, 2000, ch. 2, pp. 21–85. [19] M. Wirth, A. Singh, J. Scharer, and J. Booske, “Third-order intermodulation reduction by harmonic injection in a TWT amplifier,” IEEE Trans. Electron. Devices, vol. 49, no. 6, pp. 1082–1084, Jun. 2002. [20] S. Kusunoki, K. Kawakami, and T. Hatsugai, “Load-impedance and bias-network dependence of power amplifier with second harmonic injection,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, pp. 2169–2176, Sep. 2004. [21] C. Aitchison et al., “Improvement of third-order intermodulation product of RF and microwave amplifiers by injection,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 6, pp. 1148–1154, Jun. 2001.

Asmita Dani (S’011) received the B.Tech degree in electronics engineering from the University of Mumbai, Mumbai, India, in 2008, and the M.S.E.E. degree from the University of Colorado at Boulder in 2010, where she is currently working toward the Ph.D. degree in microwave circuits and system design. Her research interests include linearization and efficiency enhancement of power amplifiers using external harmonics, monolithic microwave integrated circuit design and analysis of communication system transmitters and receivers.

Michael Roberg (S’09) received the B.S.E.E degree from Bucknell University, Lewisburg, PA, in 2003, the M.S.E.E. degree from the University of Pennsylvania, Philadelphia, in 2006, and the Ph.D. degree from the University of Colorado at Boulder in 2012. From 2003 to 2009, he was an Engineer with Lockheed MartinMS2, Moorestown, NJ, where he was involved with advanced phased-array radar systems. His current research interests include high-efficiency microwave PA theory and design, microwave power rectifiers, monolithic microwave integrated circuit (MMIC) design, and high-efficiency radar and communication system transmitters. He is currently with TriQuint Semiconductor—Defense Products and Foundry Services, Richardson, TX, where he is involved with wideband high-efficiency GaN MMIC power amplifier design.

Zoya Popović (S’86–M’90–SM’99–F’02) received the Dipl.Ing. degree from the University of Belgrade, Belgrade, Serbia, Yugoslavia, in 1985, and the Ph.D. degree from the California Institute of Technology, Pasadena, in 1990. Since 1990, she has been with the University of Colorado at Boulder, where she is currently a Distinguished Professor and holds the Hudson Moore Jr. Chair with the Department of Electrical, Computer and Energy Engineering. In 2001, she was a Visiting Professor with the Technical University of Munich, Munich, Germany. Since 1991, she has graduated 44 Ph.D. students. Her research interests include high-efficiency, low-noise, and broadband microwave and millimeter-wave circuits, quasi-optical millimeter-wave techniques, active antenna arrays, and wireless powering for batteryless sensors. Prof. Popović was the recipient of the 1993 and 2006 Microwave Prizes presented by the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) for the best journal papers and the 1996 URSI Issac Koga Gold Medal. In 1997, Eta Kappa Nu students chose her as a Professor of the Year. She was the recipient of a 2000 Humboldt Research Award for Senior U.S. Scientists of the German Alexander von Humboldt Stiftung. She was elected a Foreign Member of the Serbian Academy of Sciences and Arts in 2006. She was also the recipient of the 2001 Hewlett-Packard (HP)/American Society for Engineering Education (ASEE) Terman Medal for combined teaching and research excellence.

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Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier Using In-Band Continuous Class-F F Mode Transferring Kenle Chen, Student Member, IEEE, and Dimitrios Peroulis, Member, IEEE

Abstract—A novel methodology for designing high-frequency broadband harmonic-tuned power amplifiers (PAs) is presented in this paper. Specifically, a hybrid PA mode, transferring between continuous inverse Class-F and continuous Class-F, is for the first time employed to design PAs with optimal performance over more than-an-octave bandwidth. A GaN PA is designed and realized based on this mode-transferring operation using a three-stage transmission-line-based low-pass matching network. Simulation and experimental results show that an in-band PA-mode transferring between continuous Class-F and continuous Class-F is successfully performed. The implemented PA achieves a measured 87% bandwidth from 1.3 to 3.3 GHz, while exhibiting a state-of-the-art performance of 10-dB gain, 60%–84% efficiency, and 10-W output power throughout this band. Furthermore, modulated evaluation is carried out using a 300-kHz bandwidth 16-quadrature amplitude-modulation signal. Good linearity performance is measured with adjacent channel power ratio from 20 to 35 dBc and an error vector magnitude of 4%–9% over the entire bandwidth. Index Terms—Broadband, continuous Class-F, continuous inverse Class-F, efficiency, GaN, harmonic tuned, low-pass matching network (MN), mode transferring, power amplifier (PA), synthesis.

I. INTRODUCTION

N

EXT-GENERATION wireless communication systems are required to operate at different communication standards/frequency bands for different applications. An ever-increasing number of high-frequency bands are being included for achieving high data transmission ratios, such as long term evolution (LTE) and worldwide interoperability for microwave access (WiMax). Consequently, power amplifiers (PAs) need to operate efficiently over a broad frequency range often spanning octave-wide bandwidths. Class-E PA mode has been extensively utilized in designing and implementing broadband PAs [1]–[3] due to its fairly simple circuitry and high efficiency. However, such a switch-mode operation fails at high frequencies (see Class-E theoretical limitation [4], [5]), Manuscript received July 10, 2012; revised September 21, 2012; accepted September 24, 2012. Date of publication October 22, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with the School of Electrical and Computer Engineering and the Birck Nano Technology Center, Purdue University, West Lafayette, IN 47906 USA (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2221142

as its parallel capacitor cannot be fully charged or discharged to support the ideal drain waveforms, leading to an efficiency degradation [6]. Harmonic-tuned PA modes, including Class-F and inverse Class-F, have been the leading candidates for realizing high-efficiency PAs at higher frequencies. These PA modes require multiple accurate harmonic terminations to present to the transistor, enforcing nonoverlapped waveforms of drain voltage and current with either square or half-sinusoidal shapes. As a result, they usually have very narrow instantaneous bandwidths in their frequency responses. To extend the operational bandwidth, advanced harmonic-tuned PA modes have been proposed and recently demonstrated, known as Class-J [7], [8], continuous Class-F [9], [10], and continuous inverse Class-F [11], [12]. These extended PA modes alleviate the precise harmonic requirements of the standard ones by offering multiple impedance solutions that can be dynamically distributed over the desired bandwidth, while maintaining the expected output power and efficiency. The harmonic requirements can be further relieved by the nonlinear output capacitor of the transistor, which assists to shape the output voltage waveform [13]–[15]. To date, several broadband PAs have been developed using the continuous PA mode with very efficient performances [15], [16], i.e., 70% average efficiencies over 50% bandwidths. However, it is worth noting that these reported PAs are designed within fairly low-frequency bands with center frequencies lower than 2 GHz, and they operate in an approximated continuous Class-F mode due to the difficulty in controlling both second and third harmonics simultaneously across a substantial bandwidth. Higher frequency designs with 80% efficiency require optimally tuned second and third harmonic impedances besides the fundamental one [17], [18]. In turn, it is of great importance to find an approach to properly control the second and third harmonics for designing and realizing broadband harmonic-tuned PAs. To accomplish this, the selection of PA mode needs to be considered together with the matching network (MN) realizability. In [19], we have proposed and experimentally demonstrated a broadband harmonic tuning method for PA design based on in-band mode transferring, which is developed from a dual-band PA design [20]. This paper significantly expands our previous work presented in [19]. First, the design concept is extended from mode transferring between Class-F and Class-F to a more general case of continuous Class-F and continuous Class-F . We also show that this generalization greatly enhances the broadband PA design space and underlines

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Fig. 1. Class-F and inverse Class-F PA topology with ideal second and third harmonic terminations.

that the design in [19] is a special case of the more general one presented here. Second, the PA design in [19] is further optimized achieving a higher measured efficiency over the entire frequency range, e.g., up to 5% improvement at the higher half band. Third, modulated-evaluation results are presented in this paper with a 0.3-MHz bandwidth quadrature-amplitude-modulation (QAM) modulated signal, showing a good potential of this PA for application in practical communication systems. II. HARMONIC-TUNED PA THEORY A. Standard Class-F/F

PA Modes

The standard Class-F PA is developed from the Class-B PA mode by loading the active device output with proper terminations at its fundamental and harmonic frequencies [21]. The half-sinusoidal current waveform, formed by the Class-B bias condition, has the following expression:

(1) The above equation (1) can be expressed using Fourier series ), given by [15] (normalized to (2) The output MN (filter) is required to provide open-circuit (O.C.) terminations at odd harmonics and short-circuit (S.C.) terminations at even harmonics, as shown in Fig. 1. Thus, a square voltage waveform is shaped, which has no overlap with the half-sinusoidal current, leading to a theoretical 100% efficiency. In practice, harmonic control is usually conducted up to the third order, as further harmonic control yields limited efficiency improvement, but significantly increased implementation difficulty. Thus, the normalized voltage waveform of a Class-F PA with a finite number of harmonic terminations can be expressed as [7] (3) The above equation is able to deliver a 90.7% efficiency at the maximum power level. The voltage and current waveforms of

Fig. 2. Theoretical voltage and current waveforms. (a) Continuous Class-F for (0.1 of steps). (b) Continuous inverse Class-F for (0.1 of steps).

the standard Class-F PA mode are plotted in Fig. 2(a), indicated by the red (in online version) (voltage) and black (current) curves. Inverse Class-F PA mode is the dual of Class-F mode. It exploits dual harmonic loading conditions with O.C. even-harmonic loads and S.C. odd-harmonic loads, as shown in Fig. 1. This forms a square-wave current and half-sinusoidal-wave voltage, which can also lead to a theoretical 100% efficiency. In the practical case of controlling three harmonics, the voltage waveform is shaped by second-harmonic peaking [12] (4) while the current waveform takes the form of (5) , , and [11]. The where voltage and current waveforms of the standard inverse Class-F PA are plotted in red (in online version) and black, respectively, in Fig. 2(b). B. Continuous Class-F/F

PA Modes

Recent investigations into continuous PA modes have demonstrated that the constant O.C. and S.C. conditions are not a unique solution for achieving optimal efficiency and output power. For the continuous Class-F mode, the voltage waveform

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in (3) can be extended by multiplying a defining term, given by [10] (6) The case corresponds to the standard Class-F mode. The range of possible values must result in an absolute positive value of the second bracket, and thus the value of in (6), as zero-crossing or negative voltage causes interaction with the knee region, and thus reduced efficiency [10]. Therefore, may vary from 1 to 1, leading to a family of voltage waveforms that offers a continuous design space with constant output performance, as shown in Fig. 2(a). Similarly, the inverse Class-F (Class-F ) mode can also be extended to continuous Class-F mode by modifying the current waveform as follows [12]: (7) Successful operation of this PA mode requires nonzero crossing current waveform, indicating a possible range of from 1 to 1 [12]. Thus, a new family of current waveforms is formed, as plotted in Fig. 2(b). A standard Class-F mode is formed when . These continuous PA modes can be realized over the target bandwidth by applying the required harmonic impedances for the different or values, which can be calculated using the following equation: (8) where represents the order of harmonic component. Here, we define as the optimum impedance of the standard Class-B mode with all harmonics short circuited, which is given by (9)

For the continuous Class-F mode, harmonic impedances are calculated using (2), (6), and (9) as follows:

(10) The calculated harmonic loads of continuous Class-F mode with are plotted in the Smith charts shown in Fig. 3(a). The harmonic loads of continuous inverse Class-F PAs are obtained in a similar manner by substituting (4) and (7) into (9), which can be expressed in the admittance format as

(11)

Fig. 3. Calculated first three harmonic loads. (a) Continuous Class-F in the . (b) Continuous inverse Class-F in the admitimpedance chart . tance chart

where . The calculated harmonic loads of continuous Class-F mode are shown in Fig. 3(b) with . A broadband PA with single continuous Class-F or F mode faces two major challenges. First, it is difficult to fit the MN’s impedance frequency response to the needed variation of the target loads with respect to or . Second, it is practically very difficult to have the third harmonic located at a constant point as it is ideally desired, i.e., O.C. for continuous Class-F or S.C. for continuous Class-F . However, it is noted from Fig. 3(a) and (b) that a combined utilization of these two continuous PA modes actually yields a further expanded design space. Also, by properly selecting the partial ranges of and , it can be easier to fit the target loads to the MN behavior. III. BROADBAND HARMONIC-TUNED PA DESIGN USING MODE TRANSFERRING A. Realization of Mode Transferring Using Multistage Low-Pass MN A proper MN is the key enabler for realizing broadband PAs. Recently, multistage low-pass topologies implemented using transmission lines (TLs) have been utilized for designing broadband high-efficiency PAs [3], [15], [22]. Design of such a complicated network requires network synthesis, which can be conducted using a real-frequency method [15], [22], [23] or methods based on low-pass filter prototypes [3]. Fig. 4(a) shows

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Fig. 4. Matching scheme. (a) Multistage TL-implemented low-pass MN and its frequency response. (b) Matching over the lower half band (continuous Class-F mode). (c) Matching over the upper half band (continuous Class-F indicates the MN impedance at the th harmonic frequencies. mode).

a typical three-stage low-pass filter MN and its illustrative frequency response. In this network, inductors are implemented by high-impedance TLs and capacitors by low-impedance O.C. stubs (STs). As shown in Fig. 4(b) and (c), a well-synthesized low-pass matching filter can provide the fundamental matching over the desired bandwidth (octave band in this research), corresponding to the filter passband. The harmonic frequencies fall in the stopband of this low-pass filter while harmonic impedances are located at the edge of Smith chart as the stopband ideally yields a reflection coefficient of . It is important to highlight that fitting the MN behavior to the target impedances of the continuous Class-F and F modes does not require the entire ranges of and . In particular, and are preferable for performing the fundamental impedance matching using this lowpass topology, indicated in Fig. 4(b) and (c). As for the specific stopband impedance trajectory of this network, the continuous F mode and continuous Class-F mode are expected to be realized across the lower and upper half parts of the entire band, respectively. For the lower half band, the second harmonic impedance of the MN [ , yellow highlighted (in online version)] tracks the target second harmonic impedance of continuous Class-F mode , as shown in Fig. 4(b). Meanwhile, the third harmonic impedance [ , green highlighted (in online version)] of this band is located in the area indicated in Fig. 4(b), covering the S.C. point. Therefore, an exact continuous inverse Class-F mode can be realized at a frequency within the lower half band which has an S.C. . As the frequency increases

to the upper half band, , highlighted in purple (in online version) in Fig. 4(c), moves clockwise and fits the target second harmonic impedance of continuous Class-F mode , while covers the blue-highlighted (in online version) region. Thus, an optimized continuous Class-F mode is realized at within the upper half band, whose third harmonic impedance is located at the O.C. point. For the rest of the band other than and , both the fundamental and second harmonics are both properly terminated, while the third harmonic is located along the edge of Smith chart, so a high efficiency can be still maintained [10]. Our previous design in [19] can be considered as a special case of this mode transferring between the continuous Class-F F modes. Fig. 4(a) underlines that and are almost located at around the middle points of the lower and upper half bands, respectively. Thus, they approximately follow the dependence of . Also, can be very close to the O.C. point, as implied in Fig. 4(a) and (b). Therefore, a standard inverse Class-F PA is formed at and a standard Class-F PA at , as is the case of [19]. With the combined utilization of continuous PA modes, the design space is greatly enlarged, while the target and can be automatically distributed to the MN’s stopband, as indicated in Fig. 4(b) and (c). Thus, in this design, the priority will be given to the fundamental impedance matching. B. Transistor Modeling and Characterization The initial target frequency range is an octave band from 1.5 to 3 GHz. Therefore, a dc–6-GHz 10-W Cree GaN transistor (CGH40010F) is used as the active device to experimentally demonstrate this design concept. As the theoretical PA mode analysis refers to the intrinsic drain plane ( -generation plane), the parasitics of the transistor need to be carefully modeled. This device consists of a CGH60015D bare chip and package. Thus, the computer-aided design (CAD)-based modeling can be conducted with a combination of the bare-chip model and the package model, which are provided by the manufacturer [24]. Compared to the packaged-transistor model, this combined model makes it easier to set up harmonic conditions in the load–pull characterization. The typical equivalent-circuit model of this transistor is shown in Fig. 5(a), indicating the intrinsic and package parasitics. and are set to around the center points In this design, of the upper and lower half bands, respectively, given by GHz and GHz. First, the desired fundamental impedances for inverse Class-F and Class-F modes are extracted from load–pull simulations using Agilent Advanced Design System (ADS) [25]. The simulated impedances at the intrinsic drain plane are purely resistive, as plotted in Fig. 5(b), and which represent the real parts of in (10) and (11). Such impedances are transferred from the and , respecintrinsic-drain plane to the package plane at tively, shown in Fig. 5(b), yielding a reference for the output MN design. Subsequently, the simulated impedances are further extended to the continuous Class-F and Class-F modes using (10) and (11), as shown in Fig. 5(c).

CHEN AND PEROULIS: DESIGN OF BROADBAND HIGHLY EFFICIENT HARMONIC-TUNED PA

Fig. 5. Transistor modeling and characterization. (a) Equivalent-circuit model of CGH40010 showing the parasitics. (b) Simulated impedances at GHz and GHz. (c) Extended impedance ranges of continuous Class-F/F modes.

C. Output MN Design The design and implementation of the low-pass MN have been studied in detail in [3]. This design follows a similar procedure, which mainly takes three steps. Step 1) Ideal-Network Synthesis: A three-stage low-pass prototype is extracted from [26], which forms an octave-bandwidth impedance transformer with 4:1 transformation ratio. The prototype is then scaled to the desired frequency and 50- reference impedance. Further, the real-to-real impedance transformer is transformed to a real-to-complex one referred to the extracted in Fig. 5(b) using an ADS optimizer. Step 2) Implementation Using TLs: The synthesized ideal network is implemented using TLs. In this design, the inductors are realized by high-impedance TLs, while the capacitors are replaced by low-impedance O.C. STs. For implementation on a Rogers 5880 PCB substrate,1 the width of TLs and STs are 20 and 90 mil, respectively, considering the fabrication tolerance and dispersive effect. The corresponding TL and ST impedances are 95 and 36 , respectively. Step 3) Post Optimization: To realize the desired transferring PA mode, the implemented OMN is connected to the parasitic model of the transistor to obtain the impedance at the intrinsic-drain plane, as shown in Fig. 6(a). This means that the parasitic network now becomes a part of the OMN. The length of each TL section is finely tuned to properly align the 1Rogers Corporation, Rogers, CT. [Online]. Available: http://www.rogerscorp.com/

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Fig. 6. Output MN design. (a) Circuit topology, (b) MN impedance. (c) Achieved impedance at intrinsic drain plane.

OMN impedance trajectory to the target impedances at both the fundamental and harmonic frequencies. The tuned OMN is finally optimized together with the actual transistor model to achieve maximum efficiency. The finalized lengths of TLs and STs are indicated in Fig. 6(a). Fig. 6(b) and (c) shows the fundamental, second-, and thirdharmonic impedances at the package plane and intrinsic-drain plane , respectively. It can be seen in Fig. 6(b) that the implemented OMN yields the desired fundamental matching over the target bandwidth since the impedance is very close to the optimal points at and . At the intrinsic drain plane, as shown in Fig. 6(c), the fundamental impedance, provided by the OMN, fits well with the target and with and , respectively. The second harmonic impedance also tracks well with the target and with the same ranges of and . The third harmonic impedance moves across the O.C. and S.C. points as expected. Specifically, an exact continuous Class-F mode is realized at GHz, while an optimal continuous Class-F mode is realized at GHz (slightly higher than the initial value). The impedance at is designed to be slightly capacitive as it leads to a higher efficiency than the pure-zero impedance [27]. This could be due to the nonlinear behavior of . IV. PA IMPLEMENTATION A. PA Design and Fabrication In [19], the input MN is implemented with a multisection TL transformer. In this study, the input MN is redesigned with a low-pass topology, which is less area consuming. A four-stage low-pass prototype is extracted from [26], as the input matching

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Fig. 7. Circuit schematic of the broadband harmonic-tuned PA.

Fig. 8. Fabricated PA circuit.

requires a larger impedance transformation ratio than the output one. This network is then implemented with TLs, the same as the ones in the output network. The schematic is shown in Fig. 7, indicating the input circuit topology and parameters of each TL sections. The entire PA is implemented by connecting the transistor to the designed input and output MNs, as illustrated in Fig. 7. and are slightly Here, the geometric dimensions of adjusted to fit the package pads of the transistor, while maintaining the MNs’ performance. The biasing networks are realized by a 17-nH inductor and 30-pF bypass capacitor. The PA is fabricated on a Rogers 5880 substrate and is mounted on a copper fixture, as shown in Fig. 8. The footprint of the fabricated PA is 60 43 mm . Compared to the previous design in [19], this design has a more compact circuit with a size reduction of larger than 30%, which is mainly due to the redesigned input MN. B. Waveform Engineering The entire PA model is established in ADS and simulated using the harmonic-balance simulator. Fig. 9(a)–(c) shows the simulated voltage and current waveforms at the intrinsic drain plane, when the broadband PA is operating at 1.8, 2.3, and 2.8 GHz with 10-W output power. Fig. 9(a) depicts a standard inverse Class-F PA waveform with half-sinusoidal

Fig. 9. De-embedded intrinsic drain waveforms of voltage and current from ADS simulation. (a) At 1.8 GHz (standard inverse Class-F). (b) At 2.3 GHz (continuous inverse Class-F). (c) At 2.8 GHz (continuous Class-F).

voltage and quasi-square-wave current, which is basically due to the specific harmonic conditions applied at this frequency. A continuous Class-F waveform is observed at 2.3 GHz, as shown in Fig. 9(b). Compared to the ideal waveform shown in Fig. 2(b), this waveform corresponds approximately to . A continuous Class-F waveform is obtained at 2.8 GHz, as shown in Fig. 9(c). This waveform corresponds to the case of a slightly negative , as indicated by the ideal waveforms in Fig. 2(a). This is the result of the harmonic [see Fig. 6(c)]. condition applied at V. EXPERIMENTAL RESULTS A. Continuous-Wave (CW) Evaluation The PA is first tested under the stimulus of a single-tone CW signal swept from 1.3 to 3.3 GHz with 0.1-GHz step. The transistor gate is biased at the threshold of 3.3 V. The drain bias voltage is set to the value that leads to the optimal power-added efficiency (PAE) in the testing, which varies at different frequencies, as shown in Fig. 10. The CW signal is generated by an Agilent E4433B signal generator and boosted by a commercial

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Fig. 10. Measured output power and the optimal drain bias point across the entire bandwidth.

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Fig. 12. Measured PAE and gain across the entire frequency range. TABLE I STATE-OF-THE-ART BROADBAND HIGH-EFFICIENCY PAs

Fig. 11. Simulated and measured efficiency over the entire bandwidth.

driver amplifier (Mini-Circuits, ZHL-16W-43+)2 to provide a sufficient input power of up to 30 dBm for the broadband testing. The PA output power is measured using an Agilent E4448 spectrum analyzer. Fig. 10 shows the measured fundamental output power from 1.3 to 3.3 GHz, which is around 10 W across the entire frequency band. Fig. 11 shows the measured and simulated efficiency within the entire frequency range. The efficiency curve has two local maxima at GHz and GHz with 80% values, corresponding to the optimal continuous inverse Class-F and Class-F modes (second and third harmonics conditions are both satisfied), respectively. The overall measured efficiency is from 60% to 84% with an average value of around 73%. Simulation agrees well with the measurement for the majority of the band, while a small difference occurs around the frequency point of mode transition (see Fig. 11). This is mainly due to inaccuracies in the modeling and fabrication. To extract the PAE, the power gain of the PA is considered and measured, which ranges from 10 to 13 dB within the entire bandwidth, as shown in Fig. 12. A PAE of 56% to 79% is measured. This design exhibits a state-of-the-art PA performance compared to the contemporary broadband PA results recently published, listed in Table I. A frequency-weighted average efficiency (FE) is introduced here to evaluate the PA efficiency together with frequency, which has often been utilized in the MTT-5 Student Design Competition and [14]. It can be seen from Table I that this paper, in particular, presents the widest 2Mini-Circuits Corporation, Brooklyn, NY. [Online]. Available: http://www. minicircuits.com/

CF: continuous Class-F, : continuous inverse Class-F, DE: drain efficiency, AE: average efficiency. FE denotes the frequency-weighted efficiency, AE center frequency GHz , similar to the metric used in MTT-5 Student PA Design Competition. The design is based on a bare-chip transistor.

fractional bandwidth and the highest frequency-weighted efficiency. We attribute this excellent performance to the combined utilization of two continuous PA modes, while other studies are all based on a single mode. The PA is also characterized under different driving powers to evaluate its dynamic performance. Fig. 13(a) and (b) shows the measured gain, drain efficiency, and PAE versus input power at 1.8 and 2.8 GHz, respectively. The gain compresses at dBm and dBm for these two frequencies, corresponding to the maximum PAE values. It is also seen from Figs. 13 that 50% efficiency can be maintained within 5 dB of output power back-off, indicating a good potential for amplifying amplitude-modulated signals. B. Modulated Evaluation To evaluate the PA performance in an actual communication system, the implemented PA is tested with a 16 quadrature-amplitude-modulation (16QAM) signal with a symbol rate of 300 ks/s, which has peak-to-average power ratio of around 7 dB. This 16QAM signal is generated by an Agilent E4438C signal generator and is amplified to a sufficient driving level by the commercial PA used in Section V-A. The biasing condition used in this measurement is also the same as that in the CW evaluation. The measured PA performance over the entire frequency band is shown in Fig. 14, indicating an average output power of around 36 dBm, average gain of around 10 dB, and average efficiency of 30%–48%. These curves have similar shapes with the corresponding CW results, as shown in Section V-A.

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Fig. 15. Measured output spectrum under stimulus of a 300-kHz 16QAM signal at 2.8 GHz.

Fig. 13. Measured PA performance versus input power at: (a) 1.8 and (b) 2.8 GHz. Fig. 16. Measured EVM and ACPR over the entire bandwidth.

Fig. 14. Measured broadband PA performance characterized under stimulus of a frequency-swept 16QAM signal. Fig. 17. Measured PA performance with a power-swept input stimulus.

Fig. 15 plots the measured output spectrum at 2.8 GHz with an average input power of 25 dBm, exhibiting an adjacent channel power ratio (ACPR) of 32 dBc measured at 150-kHz frequency offset. Compared to the input spectrum, the spectrum regrowth only leads to an ACPR increase of 13 dB at this frequency, indicating a good linearity performance of this PA. The system-level linearity performance of this PA is measured using a real-time spectrum analyzer (Tektronix RSA3408A). Fig. 16 presents the measured error vector magnitude (EVM) and ACPR across the desired bandwidth, showing an overall EVM of 3%–9% and ACPR from 36 to 20 dBc. Improved linearity is observed for the upper half band, which could be due to the mitigation of transistor’s switching behavior at higher frequencies.

Subsequently, the PA is tested with a power-swept QAM signal (from 19 to 28 dBm). Fig. 17 shows the measured average output power, gain, and efficiency with respect to the input power. The gain compression point is around 26 dBm of input power, while the maximum efficiency of 50% is achieved at input power of 28 dBm. Fig. 18 shows the linearity performance of the PA versus input power. The EVM and ACPR are at very low levels for small (EVM 4.2%, ACPR 33 dBm), and they increase sharply with input power when dBm. It can be seen from Figs. 17 and 18 that optimal input power is around 25 dBm for a QAM signal that yields a good balance between efficiency and linearity.

CHEN AND PEROULIS: DESIGN OF BROADBAND HIGHLY EFFICIENT HARMONIC-TUNED PA

Fig. 18. Measured EVM and ACPR versus input power.

VI. CONCLUSION This paper has presented an innovative approach for designing high-frequency broadband harmonic-tuned PAs based on mode-transferring between continuous inverse Class-F and continuous Class-F. Compared to the single continuous Class-F/F mode, such a hybrid PA mode can be easier to realize over an octave bandwidth. Specifically, the target fundamental and harmonic impedances can be well fitted to the frequency behavior of a three-stage low-pass MN implemented using TLs. For technology demonstration, a broadband PA was designed exploiting this method with a commercial 10-W GaN transistor. The in-band PA-mode transferring between continuous Class-F and continuous Class-F is demonstrated using waveform engineering. The fabricated PA exhibits an overall bandwidth of from 1.3 to 3.3 GHz (87% fractional bandwidth) with state-of-the-art measured performance, i.e., drain efficiency of 60%–84%, gain of 10-dB, and output power of 10 W. Moreover, modulated evaluation with a 300-kHz bandwidth 16-QAM signal reveals a good linearity performance of this PA with ACPR from 20 to 35 dBc and EVM of 4%–9% throughout the entire bandwidth. ACKNOWLEDGMENT The authors would like to thank Cree Inc., Durham, NC, for supplying the large-signal transistor models and application documents. REFERENCES [1] M. P. van der Heijden, M. Acar, and J. S. Vromans, “A compact 12-watt high-efficiency 2.1–2.7 GHz class-E GaN HEMT power amplifier for base stations,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2009, pp. 657–660. [2] A. A. Tanany, A. Sayed, and G. Boeck, “Broadband GaN switch mode class E power amplifier for UHF applications,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2009, pp. 761–764. [3] K. Chen and D. Peroulis, “Design of highly efficient broadband class-E power amplifier using synthesized low-pass matching networks,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 12, pp. 3162–3173, Dec. 2011. [4] T. B. Mader, E. W. Bryerton, M. Markovic, M. Forman, and Z. Popovic, “Switched-mode high-efficiency microwave power amplifiers in a free-space power-combiner array,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 10, pp. 1391–1398, Oct. 1998. [5] E. Cipriani, P. Colantonio, F. Giannini, and R. Giofre, “Optimization of class E power amplifier design above theoretical maximum frequency,” in Proc. Eur. Microw. Integr. Circuits Conf., Oct. 2008, pp. 514–517.

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[6] S. Jee, J. Moon, J. Kim, J. Son, and B. Kim, “Switching behavior of class-E power amplifier and its operation above maximum frequency,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 1, pp. 89–98, Jan. 2012. [7] S. C. Cripps, RF Power Amplifier for Wireless Communications, 2nd ed. Boston, MA: Artech House, 2006. [8] P. Wright, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, “A methodology for realizing high efficiency class-J in a linear and broadband PA,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 12, pp. 3196–3204, Dec. 2009. [9] V. Carrubba, A. L. Clarke, M. Akmal, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, “The continuous class-F mode power amplifier,” in 40th Eur. Microw. Conf., Oct. 2010, pp. 1675–1677. [10] V. Carrubba, A. L. Clarke, M. Akmal, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, “On the extension of the continuous class-F mode power amplifier,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 5, pp. 1294–1303, May 2011. [11] V. Carrubba, A. L. Clarke, M. Akmal, J. Lees, J. Benedikt, S. C. Cripps, and P. J. Tasker, “Exploring the design space for broadband pas using the novel “continuous inverse class-F mode”,” in 41st Eur. Microw. Conf., Oct. 2011, pp. 333–336. [12] V. Carrubba, A. L. Clarke, M. Akmal, J. Lees, J. Benedikt, S. C. Cripps, and P. J. Tasker, “The continuous inverse class-F mode power amplifier with resistive second-harmonic impedance,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 6, pp. 1928–1936, Jun. 2012. [13] J. Moon, J. Kim, and B. Kim, “Investigation of class-J power amplifier for optimized operation,” IEEE Trans. Microw. with a nonlinear Theory Techn., vol. 58, no. 11, pp. 2800–2811, Nov. 2010. [14] J. Kim, J. Kim, J. Moon, J. Son, I. Kim, J. Jee, and B. Kim, “Saturated power amplifier optimized for efficiency using self-generated harmonic current and voltage,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 8, pp. 2049–2058, Aug. 2011. [15] N. Tuffy, L. Guan, A. Zhu, and T. J. Brazil, “A simplified broadband design methodology for linearized high-efficiency continuous class-F power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 6, pp. 1952–1963, Jun. 2012. [16] V. Carrubba, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, “A novel highly efficient broadband continuous class-F RFPA delivering 74% average efficiency for an octave bandwidth,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2011, pp. 1–4. [17] P. Saad, H. M. Nemati, M. Thorsell, K. Andersson, and C. Fager, “An inverse class-F GaN HEMT power amplifier with 78% PAE at 3.5 GHz,” in 39rd Eur. Microw. Conf., Oct. 2009, vol. 1, pp. 496–499. [18] K. Kuroda, R. Ishikawa, and K. Honjo, “Parasitic compensation design technique for a -Band GaN HEMT class-F amplifier,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 11, pp. 2741–2750, Nov. 2010. [19] K. Chen and D. Peroulis, “Design of high-efficiency power ampliF mode-transferring technique,” in IEEE fier using in-band class-F MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–4. [20] Y. Ding, Y. X. Guo, and F. L. Liu, “High-efficiency concurrent dualband class-F and inverse class-F power amplifier,” IET Electron. Lett., vol. 47, no. 15, pp. 847–849, Jul. 2011. [21] F. H. Raab, “Maximum efficiency and output of class-F power amplifier,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 6, pp. 2001–2005, Jun. 2001. [22] J. Moon, J. Son, J. Lee, and B. Kim, “A multimode/multiband envelope tracking transmitter with broadband saturated amplifier,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 12, pp. 3463–3473, Dec. 2011. [23] D. Wu, F. Mkadem, and S. Boumaiza, “Design of a broadband and highly efficient 45 W GaN power amplifier via simplified real frequency technique,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2010, pp. 1090–1093. [24] R. Pengelly, B. Millon, D. Farrell, B. Pribble, and S. Wood, “Application of non-linear models in a range of challenging GaN HEMT power amplifier designs,” presented at the IEEE MTT-S Int. Microw. Symp. Workshop, Jun. 2008. [25] ADS. Agilent Technol. Inc., Santa Clara, CA, 2009. [Online]. Available: http://www.agilent.com [26] G. L. Matthaei, “Tables of Chebyshev impedance-transformation networks of low-pass filter form,” Proc. IEEE, vol. 52, no. 8, pp. 939–963, Aug. 1964. [27] P. Wright, A. Sheikh, P. J. Tasker, and J. Benedikt, “Highly efficient operation modes in GaN power transistors delivering upwards of 81% efficiency and 12 W output power,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 1147–1150. [28] P. Saad, C. Fager, H. Cao, H. Zirath, and K. Andersson, “Design of a highly efficient 2-4-GHz octave bandwidth GaN-HEMT power amplifier,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 7, pp. 1677–1685, Jul. 2010.

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Kenle Chen (S’10) received the Bachelor’s degree in communication engineering from Xi’an Jiaotong University, Xi’an, Shaanxi, China, in 2005, the Master’s degree in electronics and information engineering from Peking University, Beijing, China, in 2008, and is currently working toward the Ph.D. degree at Purdue University, West Lafayette, IN. From 2007 to 2008, he was with the Institute of Micro Electronics, National Key Laboratory of Micro/Nano Fabrication, Peking University, where his research focused on RF microelectromechanical systems (MEMS) switches, tunable filters, and vacuum packaging. He is currently with the School of Electrical and Computer Engineering and the Birck Nanotechnology Center, Purdue University. His research interests include broadband highly efficient PA design methodologies, adaptive PAs and transmitters, integration of PAs and high- filters (co-design technique), and high-power failure mechanisms of microwave devices. Mr. Chen was the recipient of the Second and Third Place Awards of the Student High Efficiency Power Amplifier Design Competition, IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) in 2012 and 2011, respectively. He was also a recipient of the 2012 IEEE MTT-S Graduate Research Fellowship.

Dimitrios Peroulis (S’99–M’04) received the Ph.D. degree in electrical engineering from The University of Michigan at Ann Arbor, in 2003. Since August 2003, he has been with Purdue University, West Lafayette, IN. He leads the Adaptive Radio Electronics and Sensors (ARES) Team, which focuses on reconfigurable analog/RF electronics for adaptive communications, signal intelligence, and harsh-environment sensors. He has been a Principle Investigator (PI)/co-PI in over 40 projects funded by government agencies and industry in these areas. Since 2007, he has been a key contributor to the Defense Advanced Research Projects Agency (DARPA) analog spectral processors (ASPs) (Phases I–III) 3:1) pre-select project, resulting in the first widely tunable (tuning range and power radio filters with unprecedented quality factors handling ( 10 W) for high-frequency applications (1–30 GHz). A wide variety of reconfigurable filters with simultaneously adaptable features including frequency, bandwidth, rejection level, filter order, and group delay have been demonstrated over the past four years. His group recently codeveloped a ground-breaking concept of field programmable filter arrays (FPFAs). Inspired by field-programmable gate arrays (FPGAs) in digital systems, FPFAs are based on a sea of coupled resonators and multiple ports in order to enable reutilization of the same adaptive resonators to support diverse needs for dissimilar systems. Arbitrary operational modes and multiple operational channels may be created and reconfigured at will. He has made significant advances in high-power high-efficiency PAs and RF CMOS integrated circuits (ICs) with high-efficiency antennas. In the areas of sensors, he has also demonstrated the first wireless battery-free high-temperature microelectromechanical systems (MEMS) sensors for health monitoring of sensitive bearings in aircraft engines. These sensors continuously monitor (RF identification (RFID) type) the true temperature of the bearing to over 300 °C or 550 °C (depending on the design) and wirelessly transmit it to a base station. These sensors are based on well-established silicon processing for low-cost high-yield manufacturing. They have demonstrated extremely robust operation for over 1B cycles and continuous loading for over three months without failure. Prof. Peroulis was the corecipient, along with his team, of Third Place in the Student PA Design Competition, 2011 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). In addition, a student design team at Purdue University, of which he was assistant team leader, was the recipient of the First Place Awards in Phases I and II of the 2007–2008 SRC/SIA IC Design Challenge by demonstrating high-efficiency chip-to-chip wireless links with -band transceivers. Further advances led to bond-wire Yagi antenna arrays with efficiencies exceeding 80%.

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High-Gain and High-Efficiency EER/Polar Transmitters Using Injection-Locked Oscillators Chi-Tsan Chen, Member, IEEE, Tzyy-Sheng Horng, Senior Member, IEEE, Kang-Chun Peng, Member, IEEE, and Chien-Jung Li, Member, IEEE

Abstract—The envelope elimination and restoration (EER) approach developed by Kahn and its modern derivative, a polar transmitter, are well recognized as highly efficient amplification schemes. This paper presents an EER/polar dual-mode transmitter using injection-locked oscillators (ILOs). For an EER operation, an ILO that is combined with a mixer and a low-pass filter in the proposed architecture extracts an envelope signal and a phase-modulated RF signal from an input RF signal with complex modulation. The phase-modulated RF signal is then amplified efficiently by a class-E power amplifier (PA). Additionally, the envelope signal is reconstructed at the PA output by modulating the supply voltage of the PA. For a polar operation, the necessary phase modulation and envelope modulation are generated in the digital domain instead. Moreover, the phase-modulated RF signal is injected into an ILO and the ILO output is amplified by a class-E PA while supply-modulated with the envelope signal. For wideband code-division multiple access (WCDMA) signals, the implemented prototype transmitter achieves a 20.8-dB gain and 44% power-added efficiency (PAE) at an average output power of 25.8 dBm. For enhanced data rates for GSM evolution signals, it delivers 26.6 dB of gain and 48.7% PAE at an average output power of 26.6 dBm. Furthermore, to compensate for the AM–AM and AM–PM distortions of the PA, the linearity is improved using static digital predistortion. Experimental results demonstrate that the proposed EER/polar transmitter using ILOs has a high gain, high efficiency, and good linearity. Index Terms—Enhanced data rates for GSM evolution (EDGE), envelope elimination and restoration (EER), polar transmitter, power amplifier (PA), predistortion, wideband code-division multiple access (WCDMA).

I. INTRODUCTION

C

HARACTERIZED by their high efficiency and high linearity, power amplifiers (PAs) are more critical than ever in modern wireless communication systems, which use nonconManuscript received July 11, 2012; revised September 24, 2012; accepted September 25, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported in part by the National Science Council, Taiwan, under Grant 100-2221-E-110-081-MY3, Grant 1002221-E-110-082-MY3, and Grant 101-2622-E-110-005-CC3. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. C.-T. Chen is with MediaTek Inc., Hsinchu, 30078, Taiwan (e-mail: [email protected]). T.-S. Horng is with the Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung 804, Taiwan (e-mail: [email protected]). K.-C. Peng is with the Department of Computer and Communication Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung 811, Taiwan (e-mail: [email protected]). C.-J. Li is with the Department of Electronic Engineering, National Taipei University of Technology, Taipei 106, Taiwan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2223712

stant envelope modulation schemes with a high peak-to-average power ratio (PAPR) [1]. To meet strict linearity requirements, conventional linear PAs (e.g., class-A and class-AB designs) often operate in the power back-off region, subsequently reducing the average efficiency. Therefore, linear amplification methods using highly efficient switch-mode or saturated PAs have been thoroughly investigated, including envelope elimination and restoration (EER) [2]–[5], linear amplification with nonlinear components (LINC) [6], polar modulation [7]–[9], hybrid EER [10], [11], and envelope tracking (ET) [12]–[15]. Among the several efficiency-enhancement schemes, EER developed by Kahn in 1952 is highly promising due to its very high efficiency with good linearity [2]. A Kahn EER transmitter operates under the principle of splitting an input RF signal with a complex modulation into an envelope signal and a phase-modulated RF signal. In a traditional approach, the former and the latter signals can be generated by sending the input-modulated RF signal into an envelope detector and a limiter, respectively. The phase-modulated RF signal is then amplified efficiently by a switch-mode PA, while preserving the phase modulation (PM) at the PA output. Additionally, the amplitude modulation (AM) is restored by modulating the supply voltage of the PA with the envelope signal. In practice, implementing an envelope detector and a limiter is a quite challenging task for a modulation signal with a high PAPR [4], [16]. Moreover, other system-related design issues include the efficiency and bandwidth of the envelope amplifier and the RF PA, the AM–AM and AM–PM distortions of the RF PA, and the time alignment of the envelope and phase signals—all of which are critical to the efficiency and linearity of the transmitter. As a modern derivative of the Kahn EER approach, polar modulation generates the modulation envelope and phase components in the digital domain. Therefore, digital signal processing can significantly improve the linearity of the transmitter at the expense of increased system complexity. Since an injection-locked oscillator (ILO) tends to follow the frequency variations of an injection signal, high-gain amplification of a frequency-modulated or a phase-modulated signal using an ILO has become a popular application [17]–[19]. Based on an injection-locking approach, switch-mode PAs have been designed recently to reduce the stringent input driving requirements, resulting in a high gain and high power-added efficiency (PAE) [20]–[22]. However, the amplitude-limiting nature of an oscillator confines most applications to amplification of constant envelope modulation signals [22], [23]. For nonconstant envelope modulation signals, applying a supply modulation scheme to an ILO provides a feasible solution [24]. In [24], a pulse-width modulated (PWM) envelope was applied to the gate bias of an ILO to switch it on and off. However, this architecture requires a high-selectivity bandpass

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Fig. 1. Block diagram of the proposed EER/polar transmitter using an ILO.

filter for restoring an envelope signal at the transmitter output. Moreover, the applicable modulation bandwidth is limited by the transient response of an ILO from switch-off to switch-on and the switching period of PWM. This paper presents a novel EER/polar dual-mode transmitter using ILOs. By combining the approaches of EER/polar modulation and injection locking, effectiveness of the implemented transmitter is demonstrated for delivering WCDMA and EDGE signals with a high gain and high efficiency. This paper has substantially expanded the earlier work [25] to improve the linearity of the proposed EER transmitter with static digital predistortion (DPD). Additionally, an extension to a polar transmitter based on the developed technology was presented as a promising alternative with enhanced linearity. II. SYSTEM ANALYSIS

Fig. 2. System model of the proposed transmitter in an EER operation.

complex-modulated input signal Cartesian coordinate components ordinate components and

A. Transmitter Architecture Fig. 1 shows the block diagram of the proposed EER/polar transmitter using an ILO. When the transmitter operates in the EER mode, an ILO that is combined with a mixer and a lowpass filter (LPF) can separate an injection signal with complex modulation into an envelope signal and a phase-modulated RF signal, subsequently dispensing with an envelope detector and a limiter required in a conventional EER transmitter. The phasemodulated RF signal is then amplified efficiently by a class-E PA, while the envelope signal is reconstructed at the PA output by modulating the supply voltage of the PA. As in the polar mode, the necessary envelope and phase signals are generated in the baseband digital signal processor (DSP). Instead, the ILO is injected with a constant envelope, phase-modulated RF signal and the PA is supply modulated with an envelope signal directly from the DSP. The mixer and LPF for envelope extraction are thus bypassed in this mode. B. Separation of Envelope and Phase Signals The EER mode and polar mode differ mainly in that an ILO is responsible for separating envelope and phase signals for the former, while not for the latter. System analysis of the proposed transmitter considers the EER mode first. Similar results for polar mode can then be derived simply by omitting the mixer and the LPF in the system shown in Fig. 1. Fig. 2 displays the system model of the proposed transmitter in an EER operation, where the mixer is treated as an ideal multiplier. The

can be expressed with and or polar coas (1)

where denotes the RF carrier frequency. The envelope signal and the phase signal correlate with the in-phase signal and quadrature signal as (2) (3) The injection signal , written as

has an instantaneous frequency (4)

represents the frequency modulation (FM) compowhere nent of . With reference to previous studies on the injection-locking phenomena in oscillators [17]–[19], [26]–[28], the instantaneous frequency of the resulting oscillator output signal under injection is given as

(5) where (6)

CHEN et al.: HIGH-GAIN AND HIGH-EFFICIENCY EER/POLAR TRANSMITTERS USING INJECTION-LOCKED OSCILLATORS

is interpreted as the locking range of the oscillator under injection, denotes the instantaneous angle between the injection signal and the inherent oscillation signal, and , , and refer to the inherent oscillation frequency of the oscillator, the oscillation amplitude, and the quality factor of its tank circuit, respectively. Equation (5) indicates that the composite frequency of an oscillator under injection is a sum of its free-running frequency and a disturbing frequency modulation equal to , in which and are regarded as the amplitude-to-frequency modulation (AM–FM) and phase-to-frequency modulation (PM–FM) mechanisms resulting from the injection signal, respectively. When an oscillator is synchronized with the injected modulation signal, the instantaneous frequency of the oscillator tends to follow the frequency variations of the modulation (i.e. FM). However, the AM–FM and PM–FM effects degrade the reproduction of the FM of the injection signal at the ILO output. Assume that the ILO is synchronized with and the distortion due to AM-FM and PM-FM is slight. The ILO output can thus be approximated as

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is synchronized to a narrowband modulation injection, the following approximations are valid for this analysis: (11) (12) Therefore, (5) can be rewritten as (13) where (14) Integrating both sides of (13) leads to the instantaneous phase of the ILO as

(7) where denotes the effective lock-in time that is introduced by the ILO. The mixer output is found as

(8) When a zero phase shift condition is applied to (8), that is,

(15) where , , and refer to an initial oscillation phase, the instantaneous phase response due to injection, and the instantaneous oscillation phase, respectively. Next, consider a time-alignment condition, in which no differential delay occurs between the envelope and phase paths. Therefore, the output signal of the transmitter in EER mode, , can be expressed as

(9) and the second-order term of (8) is filtered out by an ideal LPF, the filter output can be derived as (10) Here, is assumed to be small so that the approximation in (10) applies. Equations (10) and (7) represent the envelope signal and the phase-modulated RF signal, respectively, that are extracted from the input complex-modulated RF signal for subsequent separate amplification. Importantly, the proposed transmitter is simpler and has a higher gain than the conventional EER scheme. Moreover, the effective lock-in time of the ILO potentially alleviates the need for a bulky delay line in a conventional EER transmitter, thus favoring the integration of an EER transmitter in a single chip. C. Recombination of Envelope and Phase Signals In the following stage, the envelope signal and the phasemodulated RF signal are amplified by an envelope amplifier and a class-E PA, respectively; meanwhile the envelope modulation is reconstructed at the PA output by varying the supply voltage of the PA, as shown in Fig. 2. On assumptions that the inherent FM of a free-running oscillator caused by phase noise perturbation is far smaller than its carrier frequency and the oscillator

(16) where denotes the gain of the envelope amplifier, and and represent the AM–AM and AM–PM distortions of the class-E PA, respectively. For a polar mode operation, since the oscillator is injected with a phase-modulated RF signal, which has a constant envelope, the resulting oscillator output signal under injection is thus free of AM–FM distortion. The instantaneous phase response of the ILO due to injection is modified as (17) denotes the constant amplitude level of the injection where signal. Therefore, the output signal of the transmitter in polar mode can be expressed as

(18) Notably, the supply-modulating signal is the envelope signal from DSP, , rather than in (16).

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Fig. 4. Simplified schematic of the implemented Class-E PA.

Fig. 3. Spectra of (a) envelope, (b) phase, and (c) reconstructed complex signals of the proposed EER/polar transmitter compared with an ideal WCDMA signal source.

Based on the above analysis, Fig. 3(c) depicts the simulated spectra of the reconstructed WCDMA complex signal at the transmitter output together with its envelope and phase components in Fig. 3(a) and (b), respectively. As derived previously, the extracted envelope exhibits slight distortion during separation of the envelope and phase signals. The phase spectrum of the EER mode also reveals a higher distortion level than that of polar mode due to AM–FM effect. Consequently, as is expected, the proposed transmitter has a higher linearity in the polar mode than in the EER mode. III. SYSTEM FRONT-END MODULE IMPLEMENTATION A 1.95-GHz prototype transmitter is constructed to validate the proposed EER/polar transmitter using ILOs. The transmitter module consists of a class-E PA, a voltage-controlled oscillator (VCO) with an injection port, an envelope amplifier, and other commercially available discrete components, including couplers, a mixer with a conversion loss of 4.5 dB, and an LPF with a cutoff frequency of 30 MHz. Details of the circuitry are provided as follows. A. Class-E Power Amplifier For high-efficiency switch-mode PAs, the class-E PA is a popular topology because of its design simplicity in the load network. The classic class-E condition sets the voltage across the switch and its first derivative both equal to zero at the instant of switch-on in order to attain a theoretical 100% dc-to-RF efficiency [29]. In practice, however, several nonidealities degrade the efficiency. Fig. 4 schematically depicts the 1.95-GHz class-E PA developed in this work. The power transistor is designed in 0.15- m GaAs pHEMT technology and treated as a voltage-controlled switch with a finite switch-on resistance and finite switch-off resistance to account for transistor loss [30]. Additionally, the finite dc-feed inductance , the bondwire

Fig.

5. CW 1.2 V

measurements 5.5 V .

of

the

1.95-GHz

Class-E

PA.

Fig. 6. CW measurements of the 1.95-GHz Class-E PA in an EER/polar operation by sweeping PA drain voltage. The input power is fixed at 16.6 dBm.. (a) PAE, gain, and impedance looking into the drain of the PA. (b) AM–AM and AM–PM of the PA.

inductance , and the parasitic transistor output capacitance are also considered in the solution for maximum efficiency. Finally, the input matching network ( and ) and the output load network ( , , and ) are used to realize maximum power transfer and optimal class-E load impedance, respectively. Fig. 5 plots the measured and simulated results of the class-E PA with a drain supply voltage of 5.5 V in a continuouswave (CW) test. The PA has a maximum PAE of 57% and a power gain of 12.5 dB at an input power of 16.6 dBm. Fig. 6(a) shows the CW characteristics of the PA in an EER/polar operation by sweeping the PA drain voltage; meanwhile, the input power is fixed to 16.6 dBm for optimal PAE. The impedance

CHEN et al.: HIGH-GAIN AND HIGH-EFFICIENCY EER/POLAR TRANSMITTERS USING INJECTION-LOCKED OSCILLATORS

Fig. 7. Simplified schematic of the implemented discrete split-band envelope amplifier.

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Fig. 8. Measured and simulated conversion efficiency of the envelope amplifier versus rms output voltage while delivering envelopes of WCDMA and EDGE signals with a load resistance of 20 .

looking into the drain of the PA, which is equivalent to the load impedance of the envelope amplifier, changes from 16 to 21 when the drain voltage increases from 1 to 5.5 V. Fig. 6(b) shows the corresponding AM–AM and AM–PM characteristics of the PA. The PA generally exhibits a stronger nonlinearity at a low supply voltage than at a high supply voltage. The feedthrough effect also introduces distortion in signals with envelope zero crossings [5]. B. Envelope Amplifier As is well known, the overall efficiency of an EER/polar transmitter is the product of the efficiencies of the envelope amplifier and the power amplifier on the assumption that the power consumption of other devices in the transmitter is negligible. A high-efficiency envelope amplifier design is as important as a high-efficiency class-E PA design. Furthermore, the nonlinear transformation from the Cartesian coordinate to the polar coordinate results in substantially wider bandwidths of the envelope and phase signals than that of the baseband complex signal [10]. A conventional dc–dc converter is no longer applicable for wideband applications, such as WCDMA signals. This work designs a split-band envelope amplifier that comprises a wideband linear stage and an efficient narrowband switching stage to achieve high linearity and efficiency simultaneously [10], [31]. Fig. 7 schematically depicts the simplified discrete circuit of the envelope amplifier. The operational amplifier (op-amp) has a 3-dB bandwidth of 220 MHz, and the comparator has a hysteresis voltage of 7 mV. Fig. 8 illustrates the conversion efficiencies of the envelope amplifier at various root-mean-square (rms) output voltages while delivering the envelope of WCDMA and EDGE signals with a load resistance of 20 . The efficiency is over 60% for an rms output voltage larger than 1.5 V. Due to the static power consumption of the op-amp, the efficiency generally degrades with a decreasing rms output voltage. C. Injection-Locked Oscillator Fig. 9 shows the simplified schematic of the implemented discrete VCO with an injection port. To drive the PA properly, the VCO has an output power of 17.5 dBm at 1.95 GHz and covers the frequency from 1.91 to 2.02 GHz, with a tuning voltage ranging from 0 to 6 V. The measured dc-to-RF conversion efficiency at 1.95 GHz is 43%. Fig. 10 plots the minimum

Fig. 9. Simplified schematic of the implemented discrete VCO with an injection port.

Fig. 10. Measured and simulated injection-locking characteristic of the VCO.

injected power required to lock the VCO at various injection frequencies. According to the derivation by Huntoon [17], the distortion of an ILO that acts as a synchronous amplifier can be negligible if its locking range is at least twice larger than the peak frequency deviation of the frequency-modulated signal to be amplified. Consequently, designing an appropriate input power of the EER/polar transmitter is vital to the linearity of the system, as illustrated by simulation and measurement results in

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Fig. 11. Photograph of the implemented EER/polar transmitter front-end module.

Fig. 12. Measurement setup of the proposed EER/polar transmitter.

Section IV. Fig. 11 shows the photograph of the implemented transmitter module by integrating the above mentioned circuits. IV. SYSTEM MEASUREMENTS Fig. 12 shows the measurement setup of the proposed transmitter. Effectiveness of the prototype transmitter is demonstrated with WCDMA and EDGE signals in both EER and polar modes. This work attempts to improve the modulation accuracy of the transmitter by using lookup-table (LUT)-based DPD. The predistorter has a polar configuration. The AM LUT and the PM LUT are constructed by characterizing the AM–AM and AM–PM distortions of the transmitter, respectively [30]. WCDMA and EDGE baseband signals that incorporate the DPD function are then generated using Agilent’s Advanced Design System (ADS) and MATLAB software. Notably, the conversion between Cartesian and polar coordinates is carried out by a coordinate rotation digital computer (CORDIC) in the DSP, as similarly done in [7] and [30].

Next, the generated envelope and baseband signals are then loaded into an arbitrary waveform generator (AWG) and a vector signal generator which is also used as an RF modulator, respectively. The transmitter output signals are received by a spectrum analyzer and a vector signal analyzer for signal quality analysis. Additionally, a high-speed digitizing oscilloscope captures the instantaneous drain supply voltage of the PA and the input and output RF signals of the transmitter to observe the time alignment between the envelope and phase paths. Finally, the measuring instruments in the testbed are triggered in synchronization and accessed using a computer. A. WCDMA A WCDMA signal based on a hybrid phase-shift keying (HPSK) modulation scheme is used to test the proposed transmitter. The signal has a channel bandwidth of 5 MHz and a peak-to-average power ratio (PAPR) of 3.4 dB [32]. In the proposed architecture, differential delay is compensated for by

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Fig. 13. Measured EVM versus tuning voltage of the ILO.

Fig. 16. Measured AM–AM and AM–PM characteristics of the proposed EER/ polar transmitter with WCDMA input signals. (a) AM–AM for the EER mode. (b) AM–PM for the EER mode. (c) AM–AM for the polar mode. (d) AM–PM for the polar mode.

Fig. 14. Time-domain waveforms of the drain voltage of the PA, input RF signal, and ILO output signal.

Fig. 17. Measured output spectra of the proposed EER/polar transmitter with WCDMA input signals.

Fig. 15. Measured and simulated injection gain, EVM, and ACPR versus injected power for the proposed EER transmitter with WCDMA input signals.

using the effective lock-in time introduced by the ILO, which is adjustable by tuning the inherent oscillation frequency [28]. With an injected WCDMA power of 5 dBm, Fig. 13 shows the measured EVM versus the tuning voltage of the ILO. In a limited range of tuning voltage, EVM is optimized at a tuning voltage of 3 V. Beyond this range, the modulation quality is degraded severely because injection pulling occurs. Fig. 14 shows the time-domain waveforms of the drain voltage of the

PA, the input RF signal and the ILO output signal captured by an oscilloscope under time-alignment condition. Notably, a 30-ns delay difference between the drain voltage of the PA and the input RF signal is observed. This finding implies that the ILO contributes an effective lock-in time of 30 ns to the RF path in order to compensate for the delay mismatch. Measurement results verify the feasibility of using an ILO as a delay element for delay compensation, as described in Section II. To demonstrate the design considerations when determining the injected power of the proposed transmitter, Fig. 15 shows the relations of the injected power to the injection gain, EVM and ACPR. The injection gain is defined as the ratio of the ILO output power to the injected power. According to the measurement and simulation results, a higher injected power implies a better linearity, i.e. a lower EVM and a lower ACPR, yet

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Fig. 18. Measured efficiency, gain, ACPR, and EVM of the proposed EER/polar transmitter with WCDMA input signals. (a) Gain and efficiency for the EER mode. (b) ACPR and EVM for the EER mode. (c) Gain and efficiency for the polar mode. (d) ACPR and EVM for the polar mode.

a lower injection gain. Thus, an inherent tradeoff occurs between gain and linearity. At the designed injected WCDMA power of 5 dBm, the injection gain and EVM of the transmitter are 12.5 dB and 5.1%, respectively. Fig. 16(a) and (b) display the measured AM–AM and AM–PM characteristics of the transmitter before and after DPD for the EER mode, while Fig. 16(c) and (d) show the results for the polar mode. Notably, the injected power for polar mode is 5 dBm as well for comparison purposes. These figures reveal that the AM–FM effect of the ILO deteriorates the FM of the injected signal, subsequently resulting in wider distributions of AM–AM and AM–PM in the EER mode than that in the polar mode. This effect is particularly evident when the envelope level is close to zero crossing, causing an invalid injection-locking condition. The static DPD mainly compensates for the AM–AM and AM-PM distortions of the class-E PA. Therefore, the linearity of the proposed transmitter markedly improves in the polar mode because of the constant envelope modulation signal injection, i.e. without the AM–FM effect. Fig. 17 compares the transmitter output spectra before and after DPD for both modes at an average output power of 22.4 dBm. Fig. 18(a) depicts the measured average efficiency and gain of the transmitter in the EER mode. The PAE of the EER transmitter includes the efficiencies of the ILO, the envelope amplifier and the class-E PA. The transmitter achieves a peak PAE of 44% and a gain of 20.8 dB at the maximum average

Fig. 19. Measured and simulated injection gain, EVM, and ORFS versus injected power for the proposed EER transmitter with EDGE input signals.

output power of 25.8 dBm. Fig. 18(b) shows the measured ACPR and EVM for the EER mode. With DPD, ACPR1 can barely meet the required specification of 33 dBc in the measured average output power ranging from 15.5 to 25.8 dBm. Meanwhile, ACPR2 fails to comply with the required specification of 43 dBc. The EVMs vary from 4% to 4.7% after DPD in the identical power range. Fig. 18(c) and (d) illustrates the same measurements of the transmitter in the polar mode.

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Fig. 20. Measured AM–AM and AM–PM characteristics of the proposed EER/polar transmitter with EDGE input signals. (a) AM–AM for the EER mode. (b) AM–PM for the EER mode. (c) AM–AM for the polar mode. (d) AM–PM for the polar mode.

Although both modes have similar performance in efficiency and gain, polar mode exhibits better linearity than EER mode. According to Fig. 18(d), both ACPR1 and ACPR2 comply with the requirements of WCDMA with or without DPD. Additionally, the EVMs are below 2% after DPD in the measured average output power range. B. EDGE The ILO-based transmitter is also tested on an EDGE signal with eight phase-shift keying (8PSK) modulation. The signal has a symbol rate of 270.833 kHz and a PAPR of 3.4 dB [7]. Fig. 19 shows the injection gain, EVM, and EDGE output RF spectrum (ORFS) versus the injected power when the proposed transmitter operates in the EER mode. At the designed injected EDGE power of 0 dBm, the injection gain and EVM are 17.5 dB and 3.12%, respectively. Fig. 20(a) and (b) shows the measured AM–AM and AM–PM characteristics of the proposed transmitter before and after DPD for the EER mode, while Fig. 20(c) and (d) shows the results for the polar mode. Again, the AM–FM effect of the ILO is observed in the EER mode, resulting in a worse AM–AM and AM–PM for the EER mode than that for the polar mode. However, the distortion caused by the AM–FM effect is largely reduced, in comparison with the WCDMA case. This difference is because an EDGE signal has a smaller channel bandwidth than a WCDMA signal; in addition, zero crossing is avoided for 8PSK modulation using a rotation of radians. Fig. 21 compares the transmitter

Fig. 21. Measured output spectra of the proposed EER/polar transmitter with EDGE input signals.

output spectra before and after DPD for both modes at an average output power of 22 dBm. In a similar manner, Fig. 22(a) shows the measured average efficiency and gain of the transmitter versus the average output power in the EER mode. The transmitter achieves a peak PAE of 48.7% and a gain of 26.6 dB at the maximum average output power of 26.6 dBm. Fig. 22(b) shows the measured EDGE ORFS in decibels relative to the carrier (dBc) at 400- and 600-kHz offset and EVM for the EER mode. With DPD, the spectra due to modulation comply with the EDGE spectrum mask specification of 54 dBc at 400-kHz offset and 60 dBc

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Fig. 22. Measured efficiency, gain, ORFS, and EVM of the proposed EER/polar transmitter with EDGE input signals. (a) Gain and efficiency for the EER mode. (b) ORFS and EVM for the EER mode. (c) Gain and efficiency for the polar mode. (d) ORFS and EVM for the polar mode.

TABLE I COMPARISON OF THIS WORK WITH RECENT WORKS ON EER/POLAR/ET TRANSMITTERS

With a PWM switching frequency of 8 MHz. Predistortion.

at 600-kHz offset in the measured average output power ranging from 16.3 to 26.6 dBm. The EVMs vary from 1.4% to 1.6% after DPD in the same power range. Fig. 22(c) and (d) shows the same measurements when the transmitter operates in the polar mode. Both modes perform similarly in efficiency and

gain, and the linearity for the polar mode slightly outperforms the linearity for the EER mode. Above measurement and simulation results with WCDMA and EDGE signals indicate that the linearity of the proposed transmitter depends significantly on the ILO. Additionally,

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applying static DPD to linearize the transmitter is generally more effective in the polar mode than in the EER mode. This difference is owing to the inability of the static DPD to fully compensate for the phase perturbation caused by the AM–FM effect of the ILO. Therefore, polar mode operation is favorable for complex modulation schemes with envelope zero crossings, high PAPR, or high data rate. Otherwise, we recommend a more advanced linearization method, e.g., adaptive DPD [32], for the EER mode. Table I compares this work with other recent works on EER/ polar/ET transmitters. Because of injection locking, the ILO can simultaneously serve as a high-gain driver stage and a delay element for differential delay compensation. Therefore, the proposed transmitter has a reduced complexity while achieving a high gain and high efficiency, which are comparable to those of other transmitters. V. CONCLUSION This paper presents a novel EER/polar dual-mode transmitter using ILOs. With characterizations of an ILO under nonconstant envelope modulation injection and a class-E PA in a supply modulation scheme, the operating principles and performance of the proposed transmitter system are derived and analyzed in detail. The implemented 1.95 GHz prototype transmitter is tested with WCDMA and EDGE signals in the EER mode and in the polar mode. The transmitter achieves a gain of 20.8 and 26.6 dB, as well as an overall PAE of 44% and 48.7% at 25.8- and 26.6-dBm average output power for WCDMA and EDGE signals, respectively. The results show that the proposed EER/polar transmitter using ILOs is promising for highly efficient linear amplification, owing to its high gain, high efficiency, and simplicity of system integration. REFERENCES [1] S. C. Cripps, RF Power Amplifiers for Wireless Communications, 2nd ed. Norwood, MA: Artech House, 2006. [2] L. R. Kahn, “Single-sideband transmission by envelope elimination and restoration,” Proc. IRE, vol. 40, no. 7, pp. 803–806, Jul. 1952. [3] F. H. Raab, B. E. Sigmon, R. G. Myers, and R. M. Jackson, “L-band transmitter using Kahn EER technique,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2220–2225, Dec. 1998. [4] D. Su and W. McFarland, “An IC for linearizing RF power amplifiers using envelope elimination and restoration,” IEEE J. Solid-State Circuits, vol. 33, no. 12, pp. 2252–2258, Dec. 1998. [5] N. Wang, X. Peng, V. Yousefzadeh, D. Maksimovic, S. Pajic, and Z. Popovic, “Linearity of -band class-E power amplifiers in EER operation,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 1096–1102, Mar. 2005. [6] D. C. Cox, “Linear amplification with nonlinear components,” IEEE Trans. Commun., vol. 22, no. 12, pp. 1942–1945, Dec. 1974. [7] P. Reynaert and M. S. J. Steyaert, “A 1.75-GHz polar modulated CMOS RF power amplifier for GSM-EDGE,” IEEE J. Solid-State Circuits, vol. 40, no. 12, pp. 2598–2608, Dec. 2005. [8] J. N. Kitchen, I. Deligoz, S. Kiaei, and B. Bakkaloglu, “Polar SiGe class E and F amplifiers using switch-mode supply modulation,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 5, pp. 845–856, May 2007. [9] H.-S. Yang, J.-H. Chen, and Y.-J. E. Chen, “A polar transmitter using interleaving pulse modulation for multimode handsets,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 8, pp. 2083–2090, Aug. 2011. [10] F. Wang, D. F. Kimball, J. D. Popp, A. H. Yang, D. Y. C. Lie, P. M. Asbeck, and L. E. Larson, “An improved power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 12, pp. 4086–4099, Dec. 2006.

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[11] C.-J. Li, C.-T. Chen, T.-S. Horng, J.-K. Jau, and J.-Y. Li, “High average-efficiency multimode RF transmitter using a hybrid quadrature polar modulator,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 55, no. 3, pp. 249–253, Mar. 2008. [12] G. Hanington, P. Chen, P. M. Asbeck, and L. E. Larson, “High efficiency power amplifier using dynamic power-supply voltage for CDMA applications,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 8, pp. 1471–1476, Aug. 1999. [13] J. Choi, D. Kim, D. Kang, and B. Kim, “A polar transmitter with CMOS programmable hysteretic-controlled hybrid switching supply modulator for multistandard applications,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 7, pp. 1675–1686, Jul. 2009. [14] Y. Li, J. Lopez, P.-H. Wu, W. Hu, R. Wu, and D. Y. C. Lie, “A SiGe envelope-tracking power amplifier with an integrated CMOS envelope modulator for mobile WiMAX/3GPP LTE transmitters,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 10, pp. 2525–2536, Oct. 2011. [15] M. Hassan, L. E. Larson, V. W. Leung, D. F. Kimball, and P. M. Asbeck, “A wideband CMOS/GaAs HBT envelope tracking power amplifier for 4G LTE mobile terminal applications,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 5, pp. 1321–1330, May 2011. [16] T. Sowlati, Y. Greshishchev, and C. A. T. Salama, “Phase-correcting feedback system for Class E power amplifier,” IEEE J. Solid-State Circuits, vol. 32, no. 4, pp. 544–550, Apr. 1997. [17] R. D. Huntoon and A. Weiss, “Synchronization of oscillators,” Proc. IRE, vol. 35, no. 12, pp. 1415–1423, Dec. 1947. [18] R. C. Mackey, “Injection locking of klystron oscillators,” IRE Trans. Microw. Theory Tech., vol. MTT-10, no. 4, pp. 228–235, Jul. 1962. [19] H. L. Stover and R. C. Shaw, “Injection-locked oscillators as amplifiers for angle-modulated signals,” in G-MTT Int. Symp. Dig., 1966, pp. 60–66. [20] K.-C. Tsai and P. P. Gray, “A 1.9-GHz, 1-W CMOS class-E power amplifier for wireless communications,” IEEE J. Solid-State Circuits, vol. 34, no. 7, pp. 962–970, Jul. 1999. [21] H.-S. Oh, T. Song, E. Yoon, and C.-K. Kim, “A power-efficient injection-locked class-E power amplifier for wireless sensor network,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 4, pp. 173–175, Apr. 2006. [22] J.-S. Paek and S. Hong, “A 29 dBm 70.7% PAE injection-locked CMOS power amplifier for PWM digitized polar transmitter,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 11, pp. 637–639, Nov. 2010. [23] J. Pandey and B. P. Otis, “A sub-100 W MICS/ISM band transmitter based on injection-locking and frequency multiplication,” IEEE J. Solid-State Circuits, vol. 46, no. 5, pp. 1049–1058, May 2011. [24] Y.-S. Jeon, H.-S. Yang, and S. Nam, “A novel high-efficiency linear transmitter using injection-locked pulsed oscillator,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 4, pp. 214–216, Apr. 2005. [25] C.-T. Chen, Y.-C. Lin, T.-S. Horng, K.-C. Peng, and C.-J. Li, “Kahn envelope elimination and restoration technique using injection-locked oscillators,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Jun. 2012, pp. 1–4, Session WEPG-16. [26] R. Adler, “A study of locking phenomena in oscillators,” Proc. IRE, vol. 34, no. 6, pp. 351–357, Jun. 1946. [27] L. J. Paciorek, “Injection locking of oscillators,” Proc. IEEE, vol. 53, no. 11, pp. 1723–1727, Nov. 1965. [28] C.-T. Chen, C.-H. Hsiao, T.-S. Horng, K.-C. Peng, and C.-J. Li, “Cognitive polar receiver using two injection-locked oscillator stages,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 12, pp. 3484–3493, Dec. 2011. [29] N. O. Sokal and A. D. Sokal, “Class E-a new class of high-efficiency tuned single-ended switching power amplifiers,” IEEE J. Solid-State Circuits, vol. SSC-10, pp. 168–176, Jun. 1975. [30] C.-T. Chen, C.-J. Li, T.-S. Horng, J.-K. Jau, and J.-Y. Li, “Design and linearization of class-E power amplifier for nonconstant envelope modulation,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 4, pp. 957–964, Apr. 2009. [31] Y. Li, J. Lopez, D. Y. C. Lie, K. Chen, S. Wu, T.-Y. Yang, and G.-K. Ma, “Circuits and system design of RF polar transmitters using envelope-tracking and SiGe power amplifiers for mobile WiMAX,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 58, no. 5, pp. 893–901, May 2011. [32] C. D. Presti, F. Carrara, A. Scuderi, P. M. Asbeck, and G. Palmisano, “A 25 dBm digitally modulated CMOS power amplifier for WCDMA/ EDGE/OFDM with adaptive digital predistortion and efficient power control,” IEEE J. Solid-State Circuits, vol. 44, no. 7, pp. 1883–1896, Jul. 2009.

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Chi-Tsan Chen (S’07–M’12) was born in Taichung, Taiwan, in 1982. He received the B.S.E.E., M.S.E.E., and Ph.D. degrees from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2005, 2007, and 2012, respectively. He is currently a Senior Engineer with MediaTek Inc., Hsinchu, Taiwan. His research interests include RF power amplifiers, highly efficient and linear transmitter design, and low-power transceivers.

Tzyy-Sheng Horng (S’88–M’92–SM’05) was born in Taichung, Taiwan, on December 7, 1963. He received the B.S.E.E. degree from National Taiwan University, Taipei, Taiwan, in 1985, and the M.S.E.E. and Ph.D. degrees from the University of California, Los Angeles, in 1990 and 1992, respectively. Since August 1992, he has been with the Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, where he was the Director of the Telecommunication Research and Development Center (2003–2008) and Director of the Institute of Communications Engineering (2004–2007), and where he is currently a Distinguished Professor. He has authored or coauthored over 200 technical publications published in refereed journals and conferences proceedings, mostly in IEEE publications. He holds over ten patents. His research interests include RF and microwave ICs and components, RF signal integrity for wireless system-in-package, digitally assisted RF technologies, and green radios for cognitive sensors and Doppler radars. Dr. Horng has served on several Technical Program Committees of international conferences including the International Association of Science and Technology for Development (IASTED) International Conference on Wireless and Optical Communications, the IEEE Region 10 International Technical Conference, the IEEE International Workshop on Electrical Design of Advanced Packaging and Systems (EDAPS), the Asia–Pacific Microwave Conference, the IEEE Radio and Wireless Symposium, and the Electronic Components and Technology Conference. He has also served on the Project Review Board in the Programs of Communications Engineering and Microelectronics Engineering at the National Science Council, Taiwan. He was the recipient of the 1996 Young Scientist Award presented by the International Union of Radio Science, the 1998 Industry-Education Cooperation Award presented by the Ministry of Education, Taiwan, and the 2010 Distinguished Electrical Engineer Award presented by the Chinese Institute of Electrical Engineering, Kaohsiung Branch, Taiwan. Recently, he was awarded with the 2011 Advanced Semiconductor Engineering Inc. Chair Professorship and the 2012 Outstanding Research Award at the National Sun Yat-Sen University. He is the Founder Chair of the IEEE Microwave Theory and Techniques Society (MTT-S) Tainan Chapter and currently an associate editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and a member of the IEEE MTT-S Technical Committee MTT-10 and MTT-20.

Kang-Chun Peng (S’00–M’05) was born February 18, 1976, in Taipei, Taiwan. He received the B.S.E.E., M.S.E.E., and Ph.D. degrees from the National Sun Yat-Sen University, Kaohsiung, Taiwan, in 1998, 2000 and 2005, respectively. He is currently an Assistant Professor with the Department of Computer and Communication Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung, Taiwan. His current research interests are in the area of elta–sigma modulation techniques, low-noise phase-locked loops, low-power voltage-controlled oscillators, and modulated frequency synthesizers.

Chien-Jung Li (S’07–M’10) was born in Tainan, Taiwan, on October 26, 1979. He received the B.S.E.E. and Ph.D. degrees from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2002 and 2009, respectively. He was a Postdoctoral Fellow with the Department of Electrical Engineering, National Sun Yat-Sen University, in 2009. Following his postdoctoral position, he joined MediaTek Inc., Hsinchu, Taiwan, as a Senior Engineer, in 2010. He is currently an assistant professor with the Department of Electronic Engineering, National Taipei University of Technology, Taipei, Taiwan. His research interests include power-amplifier linearization techniques, frequency synthesizer designs, RF sensing circuits, injection-locking techniques, and LO pulling issues in direct-conversion transceivers.

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A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer Adrian Tang, David Murphy, Frank Hsiao, Gabriel Virbila, Yen-Hsiang Wang, Student Member, IEEE, Hao Wu, Yanghyo Kim, and Mau-Chung Frank Chang, Fellow, IEEE

Abstract—A -band CMOS transmitter is presented with an integrated injection-locked frequency-tripling synthesizer, digital control, and an on-chip antenna. It employs an IF feed-forward pre-distortion scheme, which improves gain compression of the transmitter to provide an overall higher linearity gain profile, allowing reduced power back-off for higher peak-to-average modulation schemes. The integrated -band transmitter consumes 347 mW and occupies 1800 1500 m of silicon area. The proposed transmitter delivers 0.4 dBm of effective isotropic radiated power with a saturated power on-chip of at least 12.2 dBm. The transmitter has a peak power-added efficiency (PAE) of 4.8% with power delivered to the antenna and a peak PAE of 0.31% when considering radiated power. Index Terms— -band transmitter, digital-controlled millimeter wave, feed-forward linearization, on-chip antenna.

I. INTRODUCTION

R

ECENT advances in silicon technology have enabled the possibility of CMOS-based gigabit/second rate millimeter-wave transceivers beyond the 100-GHz frequency range [1]–[3] While digital and mixed-signal techniques to support gigabit/second communications are quite mature, the design of RF front-ends beyond -band is a relatively new topic. Design of power amplifiers (PAs) that deliver enough output power to maintain the required link signal-to-noise ratio (SNR) is challenging, especially at frequencies approaching 150 GHz as the available device gain is low. One difficult challenge of CMOS millimeter-wave transmitters operating beyond 50 GHz is that amplifier compression is quite soft [4]. This means that the gain begins to compress at signal levels far below saturation. Power-amplifier compression directly contributes to the transmitter’s overall AM–AM characteristic, a major source of error-vector magnitude (EVM) degradaManuscript received July 07, 2012; revised September 18, 2012; accepted September 27, 2012. Date of publication November 19, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. A. Tang was with the Department of Electrical Engineering, University of California at Los Angeles (UCLA), Los Angeles, CA 90001 USA. He is now with the Jet Propulsion Laboratory (JPL), Pasadena, CA 91109 USA. D. Murphy is with the Broadcom Corporation, Irvine, CA 92602 USA. F. Hsiao, G. Virbila, Y.-H. Wang, H. Wu, Y. Kim, and M.-C. F. Chang are with the Department of Electrical Engineering, University of California at Los Angeles (UCLA), Los Angeles, CA 90001 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222916

Fig. 1. (a) Typical gain compression profile for a CMOS millimeter-wave PA as bias current is increased. (b) Proposed compression profile showing intentionally removed gain at small-signal levels and dynamic biasing.

tion and lowered bit-error-rate performance, especially when modulations with high peak-to-average ratios are used. While digital-pre-distortion (DPD) is common at lower frequencies, the high symbol rate and wide channel bandwidth of gigabit/second millimeter-wave communication makes implementation increasingly difficult due to the need for wideband matching and high-speed digital-to-analog converters (DACs). The local oscillator (LO) remains another critical source of error vector magnitude (EVM) degradation in gigabit/second communications where the integrated phase across relatively wide channels leads to large rotations of the signaling constellation. While the carrier frequency is quite high, the available reference frequencies from crystal oscillators remain quite low, leading to large phase multiplication factors, making the design of low phase-noise frequency synthesizers challenging beyond -band ranges. II. DYNAMIC BIASING IN CMOS PAS Fig. 1(a) shows the gain compression profile for a typical CMOS millimeter-wave PA as the static dc bias current is increased. While the saturated power does increase as the dc bias current is raised, the back-off point where the compression begins remains almost constant, and limits the linearity improvement that can be achieved. Instead of adjusting the bias to a fixed value, we propose to construct the transmitter with the compression profile that is shown in Fig. 1(b). By intentionally removing some of the small-signal gain and then adjusting the bias dynamically based on the signal’s power envelope, the linear range of the PA can be artificially increased, allowing operation to occur closer to the saturated power level. Previously, this dynamic bias behavior was achieved using the architecture shown in Fig. 2 [5]. In this scheme, an envelope detector is used at the output of the PA and a dynamic bias

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Fig. 2. Dynamic biasing approach from [2] where an envelope detector is used at the PA output to produce a dynamic bias signal.

Fig. 3. Block diagram of the proposed IF feed-forward dynamic biasing millimeter-wave transmitter chain showing feed-forward pre-distortion block.

signal is derived from the detector output to compensate for the amplifier compression. While this approach performs well at the industrial–scientific–medical (ISM) 60-GHz band application in [2] with a 1-GHz channel, the limited time constant of the feedback loop makes it difficult to achieve large bandwidths at -band, and also makes the feedback stabilization more difficult, as -band PAs typically have a larger number of stages. We propose to instead employ a feed-forward architecture to overcome the difficulties associated with placing a feedback loop around the PA. III. PROPOSED TRANSMITTER CHAIN Fig. 3 shows the block diagram of the millimeter-wave transmitter chain and integrated frequency synthesizer with the proposed feed-forward pre-distortion scheme. In this architecture, the IF signal can be fed in from an external source or the transmitter can be used for direct conversion double-sideband (DSB) modulations. In this transmitter, a five-stage PA brings the transmitted signal up to full power 12 dBm for transmission by the antenna. The first four stages of the PA are controlled by calibration DACs, which can set the bias current level of each stage. Each DAC is a simple resistor-to-resistor (R2R) configuration with 8 bits of resolution. Since the DACs only provide dc control

levels, the dynamic performance (signal-to-noise plus distortion ratio) is not critical and the RC time constants can be made large to save power. Additionally since the PA’s sensitivity to the static bias is limited, the DACs do not require a high degree of static matching, and thus integrated and differential nonlinearity beyond 4–5 least significant bits (LSBs) can be tolerated. The IF feed-forward pre-distortion block first takes the magnitude of the IF signal using an envelope detector, then adjusts the detector’s output with gain and offset properties to provide the dynamic biasing signal to the output stage of the PA. It also contains two DACs, one for the offset adjustment and the other for the gain adjustment. While in this prototype architecture we use a single DSB IF to make testing easier, it is readily adaptable to quadrature IF architectures [in-phase/quadrature (IQ)] by having two pre-distortion blocks for I and Q channel and then summing the resulting signals. Fig. 4 contains the IF feed-forward pre-distortion circuit used to cancel the soft compression of the PA. The circuit first employs an envelope detector composed of Q1 and Q2 and loaded by current mirror Q4–Q5 to extract the envelope of the IF signal. Device Q3 is controlled by the “Gain” DAC and steals a percentage of the current away from the current mirror to provide gain control of the envelope signal. Since the output of the current mirror is single ended, the dc common mode (CM) cannot be extracted by conventional differential approaches, and using an RC filter would require large capacitor area for the time constants involved. Instead we use the replica circuit shown on the right of Fig. 4 that has a dc voltage tracked by the op-amp. The output stage of the op-amp is duplicated by Q6 and Q7, which sets the dc voltage at the output of the pre-distortion block. The dc voltage is selected from the “offset” DAC by providing the tracking reference voltage to the opamp. When the IF input signal is small, the added offset voltage is much larger than the envelope detector output, and thus the “offset” DAC dominates the shaping of the PA compression at low output powers. When the IF swing is large, the envelope detector output is much larger than the offset and thus the “gain” DAC dominates the shaping of the PA compression at high power levels. This allows two degrees of freedom to tune the shape of the PA’s compression. The envelope detection circuit and its replica must be symmetric in layout to obtain the necessary matching. As the pre-distortion block is digitally programmable over a wide range of gains and offsets, its own path linearity has a little impact on the final optimized transmitter linearity. Also, as the gain stage in the pre-distortion block is implemented as a current mirror, as opposed to a voltage mode amplifier, the distortion levels remain low at the cost of some power consumption. Fig. 5 shows the schematic of the transmitter mixer and the millimeter-wave PA in which all stages are transformer coupled. The compensation signal for the fifth stage of the PA and DAC generated bias voltages on stages 1–4 are fed through the center-tap of the winding connected to the input of each stage. This allows modulation of the bias without disturbing the differential-mode RF signals. Also shown are the internal structure of the R2R DACs, and all RF device dimensions in micrometers. All RF devices have 65-nm channel lengths. Transformer-based coupling also offers the advantage that the stages are not dc coupled, making the transmitter inherently stable close to dc. The

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Fig. 4. Schematic diagram of the pre-distortion block showing dc replica circuit and calibration DACs.

Fig. 5. RF mixer and PA schematic showing transformer coupling for RF connections and center-tap coupling for IF feed-forward signal connections and DAC bias voltage connections.

Fig. 7. Cascaded divider PLL for -band requiring three different injection locked dividers (A, B, C) in cascade to provide a low enough frequency input to the CML programmable divider.

and impedance matching. The resistivity of the silicon is approximately 10 cm based on foundry models. While the authors are unable to measure the radiated pattern, the simulated directivity of the antenna is 6 dBi including feed-line and substrate losses. IV. FREQUENCY MULTIPLIED SYNTHESIZERS

Fig. 6. On-chip half-wave patch antenna and dimensions. Impedance matching balun is also shown.

LO input of the mixer is also transformer coupled and the CM voltage on the LO port of the mixer is programmable via an additional R2R DAC. The transmitter antenna is implemented as a half-wave patch antenna placed directly over the substrate, as shown in Fig. 6, and coupled to the PA using an on-chip balun, which provides differential to single-ended conversion

The -band (42–48 GHz) phase-locked loop (PLL) previously presented in [6] for 60-GHz applications uses an injection-locked divider and injection-locked output buffer in conjunction with a current-mode logic (CML) programmable frequency divider. Tuning for the divider, an injection-locked buffer and a primary voltage-controlled oscillator (VCO) are controlled by digitally controlled artificial dielectric (DiCAD) elements [7]. While this architecture delivers excellent performance at 42–48 GHz, it becomes problematic as the frequency is increased up to -band since the maximum input frequency of the CML-based programmable divider is limited to 25 GHz at most in 65-nm CMOS technology. As shown in Fig. 7, using a regular cascade of injection-locked frequency dividers (ILFDs) for -band would require at least three ILFD stages to divide the -band carrier signal down to a frequency that the CML can readily accept 25 GHz . Such a high count of slave oscillators could potentially limit the tuning range of the synthesizer and create difficulty ensuring that the frequency alignment was sufficient to maintain the locked condition. The large process variation

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Fig. 8. (a) Direct harmonic tripling with a millimeter-wave amplifier. (b) ILFT with an oscillator.

associated with deep-sub-micrometer CMOS technology will further exacerbate the frequency alignment. An additional difficulty is that varactors provide very low- beyond 100 GHz, causing a considerable reduction in oscillator swing and potentially creating difficulties in achieving VCO startup. For this reason, high-frequency oscillators beyond -band (110 GHz) typically offer very narrow tuning ranges of only 1%–2%. One common technique to overcome the challenges of frequency synthesis above 100 GHz is that of frequency multiplication. In frequency multiplication, a low-frequency synthesizer is first used to generate a stable carrier, and then the frequency is multiplied through manipulation of harmonics generated by introducing a nonlinear element. One of the most practiced frequency multiplier approaches is the direct harmonic tripler shown in Fig. 8(a). In this approach, a lower frequency millimeter-wave signal (48 GHz) is fed into a nonlinear element denoted as the “3X” unit in the block diagram. The output of this block is tuned to the third harmonic, allowing extraction of the high-frequency (144 GHz) tone. The key challenge to this approach is that the generated harmonics will be at much lower voltage swings as the fundamental to harmonic conversion is quite lossy (on the order of 10–15 dB in the -band range). To alleviate this problem, a PA often called an “LO amplifier” is used to restore signal swing. While this technique is straightforward, it has the major disadvantages of large area and high power consumption as the transmitter now needs two PAs, one in the transmit chain and another in the LO chain. Alternatively, the architecture in Fig. 8(b) commonly called sub-harmonic injection locking or injection-locked frequency tripling (ILFT), proposed in [8] and recently demonstrated with excellent results at -band in [9], uses an oscillator operating at three times the input frequency. The third harmonic generated in the nonlinear “3X” block will injection lock the oscillator to restore the signal swing. This has the major advantage of being able to restore the voltage swing in only one stage without the associated power consumption of an additional millimeter-wave amplifier. One limitation, however, is that the injection-locked approach provides less tuning range because the locked oscillator range is relatively small, as mentioned earlier. While this is very problematic for highly channelized applica-

Fig. 9. Block diagram of the proposed

-band frequency synthesizer.

tions such as 60-GHz communication systems, we target wideband gigabit/second single-channel communications at -band, and therefore can escape by requiring only a fixed LO. The synthesizer architecture for the proposed transmitter is shown in Fig. 9. The architecture first uses the original -band (42–48 GHz) PLL with a 50-MHz reference and a single ILFD used to divide the carrier from 48 to 24 GHz to provide a lowfrequency input for the programmable CML divider. An injection-locked buffer is inserted between the VCO and divider and used to drive the input of a -band ILFT. Frequency alignment of the buffer is relatively easy as the frequency is identical to the VCO making the passives and devices used in both oscillators quite similar. For the -band application, the -band PLL will nominally run at 46–48 GHz. The buffer drives an ILFT containing a nonlinear amplifier, which generates a large third harmonic at 138–144 GHz used to injection lock an oscillator (also running at 138–144 GHz). The ILFT restores signal swing and also filters out the lower 44–48-GHz fundamental tone. Finally, the ILFT output is provided by a small singlestage output amplifier used to boost the LO power and isolate the oscillator’s tank from the low mixer impedance. While the proposed frequency synthesizer still contains many injection-locked stages, it removes one level of injection locking versus the original cascaded divider architecture. Additionally, since the high-frequency -band components are not directly inside the synthesizer’s feedback loop, the associated narrow locking range and limited output swing have little effect on the PLL’s locking conditions. Since the original PLL can tune from 42 to 48 GHz, the generated third harmonic can sweep 3X this wide range (126–144 GHz), relaxing the frequency alignment at -band. The synthesizer will lock provided the -band oscillator’s free-running frequency is within this range. The only critical alignment at -band is the frequency of the output LO boosting amplifier must be well aligned with the -band oscillator’s locking range to provide useful output swing necessary to drive the transmit mixer.

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Fig. 10. (a) Proposed harmonic tripler circuit with complementary diode connected devices Q1 and Q3 to improve harmonic generation. (b) Simulated output voltage spectrum with and without Q1 and Q3.

V.

-BAND INJECTION-LOCKED FREQUENCY TRIPLER

Previously in [9], a common emitter stage using an SiGe HBT device was employed to provide the nonlinearity required to generate odd harmonics. Unlike bipolar devices, CMOS common source stages exhibit very soft-voltage waveform clipping, providing limited harmonic generation. For this reason, the harmonic generation circuit shown in Fig. 10(a) is used in the proposed -band synthesizer. The employed tripler circuit contains complementary diode connected devices Q1 and Q3 to help create waveform clipping at both the lower and upper half of the voltage swing and further increase generation of third-order harmonic distortion components. Fig. 10(b) shows the simulated spectrum at the output with and without Q1 and Q3 present. Through the added nonlinearity of Q1 and Q3, the third harmonic output voltage is increased by 11.4 dB in simulation. Note that the input is from an oscillator-based buffer so the input swing approaches twice the supply voltage, causing Q3 to clamp when . Series device Q1 artificially increases the perceived of device Q2 causing distortion at the bottom of each cycle. While the output power level is small, it is still sufficient to injection lock the following -band oscillator stage. The injection-locking range of an oscillator can be described by , where is the injected current, is the oscillator current, is the center frequency, and is the quality factor of the oscillator tank. To ensure locking of the proposed -band synthesizer, we control the oscillator current with a small R2R 8-bit DAC, as shown in Fig. 11. This allows the current to be calibrated for maximum locking range while still ensuring correct startup occurs. The oscillator tank is transformer coupled to provide output to the LO booster amplifier. A second DAC provides CM control of the LO booster output via the center tap of an output transformer to provide the correct dc levels for the input port of the mixer. Note the -band oscillator contains no varactor or tuning capacitors, as their inclusion would degrade voltage swing and possibly influence oscillator startup. Also note the tuning range of the -band PLL’s third harmonic (126–144 GHz) is much wider than the actual lock range of the ILFT (142.3–144.5 GHz measured).

Fig. 11. -band ILFT section of proposed synthesizer showing oscillator, con, LO booster, and DAC for CM adjustment. trol DAC for

Fig. 12. Probe-based test chip for power measurement containing limeter-wave power amplifier and -band oscillator.

-band mil-

VI. MEASUREMENTS First, to verify the output power of the transmitter chain, a standalone chip was constructed with the millimeter-wave PA driven by the oscillator from the ILFT, as shown in Fig. 12. Since the input of the CMOS millimeter-wave PA is a voltage mode port and not matched to 50 , this approach makes power testing straightforward for probe testing. An on-chip thru-line was used in conjunction with a -band source from VDI Inc., Charlottesville, VA, a PM4 power meter also from VDI Inc., and WR-6.5 probes from Cascade Microtech, Beaverton, OR, to first estimate the insertion loss of the probes and test setup. This process is illustrated in Fig. 13 and relies on two simple

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Fig. 13. Test setup calibration at

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-band for power measurement.

assumptions: that test setup is symmetric, and that the insertion loss of the on-chip thru line is negligible. Since the probes and waveguide sections are identical and the thru ine is only 100 m in length, these assumptions should be valid. Once the power calibration is completed, the power from the PA can be directly measured with the Erickson meter, as shown in Fig. 14. We also show the output from the test chip on a spectrum analyzer with a -band mixer (also from VDI Inc.). Note that the output levels on the spectrum analyzer are not correctly calibrated since we are unsure of the mixer conversion loss/gain. Only the PM4 reading is valid. The spectrum analyzer is only used to confirm the power being measured is in the 145-GHz range. With the calibrated insertion loss of 4.14 dB, the reading of 6.404 mW (8.06 dBm) can be used to compute the actual PA output of 12.2 dBm. One uncertainty is that the oscillator output may not be completely saturating the PA, thus this test ensures that the saturated power is at least 12.2 dBm, but in fact, it may be higher. Also note that only a ground–signal–ground (GSG) probe was available to probe our GS pads. The calibration procedure should still take this mismatch into account, as the setup was symmetric. The reported frequency from the spectrum analyzer is 146.1 GHz, 2 GHz higher than where the oscillator operates within the ILFT of the transmitter chip. The LO booster is constructed from larger devices than the first stage of the PA so the oscillator in the test-chip experiences less capacitive loading, which accounts for the frequency shift. Fig. 15 shows a die photograph of the proposed transmitter implemented in 65-nm CMOS indicating the location of key blocks. The transmitter chip is wire bonded to a printed circuit board (PCB) with the antenna surface facing in the upward direction. The PCB provides dc connectivity for supply and bias, USART connectivity for controlling the calibration DACs from a PC, and connectivity to provide the IF signal into the transmitter. In a radiation-based measurement using the same PM4 power meter as in the probe testing combined with a standard -band gain horn antenna from VDI Inc., we measured a saturated effective isotropic radiated power (EIRP) of 0.4 dBm using the calculated path loss for a distance of 5.0 cm from the chip surface and the known gain of the horn. Using the entire chip power consumption of 347 mW provides a PAE of 0.31%. Using the same setup with the same PM4 power meter, the input power at the IF of the transmitter is swept and the transmitter gain is computed at each step based on the measured EIRP and calculated path loss. Fig. 16 demonstrates the effect of changing the offset setting of the pre-distortion block on the

Fig. 14. Power measurement of the standalone power testing chip containing the -band millimeter-wave PA.

Fig. 15. Die photograph of the proposed millimeter-wave transmitter showing the location of key blocks and the on-chip antenna.

overall gain compression while the gain setting is held at 50% of full scale. As expected, the offset setting drastically affects the small-signal gain, while having limited effect on the large-signal gains.

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Fig. 16. Radiated output power and gain compression of the proposed transmitter as the pre-distortion offset control is varied.

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Fig. 18. Optimized gain compression compared with a static dc bias showing a 6.5 dB improvement in P1 compression point.

Fig. 19. Measured carrier phase noise at transmitter chain output. Fig. 17. Radiated output power and gain compression of the proposed transmitter as the pre-distortion gain control is varied.

Fig. 17 demonstrates the effect of changing the pre-distortion block’s gain setting on the overall gain compression while the offset setting is held at 50% of full scale (500 mV). Also as expected, the pre-distortion gain setting has little influence on the small-signal gain (as there is not enough signal swing at the IF to affect the pre-distortion block’s output voltage). The pre-distortion gain setting, however, has a large influence on the large-signal gain of the transmitter, although it is unable to change the saturated power level, slightly reducing the overall PAE. By first setting the pre-distortion offset to 850 mV and then setting the gain to zero, we can effectively bias the PA statically at 850 mV. We then compare that with optimized predistortion gain and offset settings in Fig. 18. Through the use of the proposed IF feed-forward pre-distortion scheme, we see that the P1 dB point has been improved by 6.5 dB. Finally, although we cannot directly access the frequency synthesizer in our design from the outside, we can measure the phase noise at the transmitter output when a large dc voltage is applied to the IF. While the transmit chain will contribute noise

to the measurement, this should be far below the phase noise of the synthesizer at small frequency offsets around the carrier. Using the same WR-6.5 probes and VDI Inc. mixer as before, we directly measure the phase noise on the spectrum analyzer and plot the results in Fig. 19. In the phase-noise measurement, we see that the in-band noise is actually dominant over the noise of the injection-locked oscillator, indicating that the charge pump or phase detector noise sources may dominate in the lower -band PLL. Similar results were reported in [6], which uses a variant of the -band PLL in this study. The overall phase noise is comparable to other PLLs providing carriers in similar frequency ranges [10], [11]. VII. SUMMARY The proposed IF-envelope feed-forward pre-distortion transmitter is realized to improve the transmitter gain compression and increase the P1 compression point by 6.5 dB when implemented in a 65-nm CMOS technology. The transmitter is also integrated with an injection-locked frequency-tripler-based synthesizer providing 82.5-dBc/Hz phase noise at 1-MHz frequency offset, which is suitable for wideband gigabit/second

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communication. Also demonstrated is a digital technique for calibration of high-frequency millimeter-wave front-ends using 8-bit DACs to adjust bias currents for optimization of stage gain. The proposed transmitter offers 15 GHz of bandwidth centered between 135–150 GHz, with a saturated output power of 12.2 dBm measured, and saturated EIRP of 0.4 dBm. The entire transmitter consumes 347 mW of dc power and occupies 1800 m 1500 m of silicon area including an integrated patch antenna. When power delivered to the antenna is considered, a peak PAE of 4.8% is achieved and when EIRP is considered, the peak PAE is 0.31%. ACKNOWLEDGMENT The authors would like to acknowledge TSMC, Hsinchu, Taiwan, for their excellent 65-nm foundry support, as well as Dr. Z. Xu, HRL Laboratories, Malibu, CA, and Prof. Qun Gu, University of Florida, Gainesville, for several excellent technical discussions.

Adrian Tang received the Ph.D. degree in electrical engineering from the University of California at Los Angeles (UCLA). He is currently a Postdoctoral Scholar with the NASA Jet Propulsion Laboratory, Pasadena, CA, where he is involved with working with 680-GHz imaging radars. He has coauthored over 30 papers on RF, millimeter-wave imaging, and communication systems in CMOS technology. Dr. Tang was the recipient of the 2012 Ph.D. Distinguished Ph.D. Dissertation Award of the UCLA Henry Samueli School of Engineering and the Broadcom University Research Award.

David Murphy received the B.E. and M.Eng.Sc. degrees from the University College Cork, Ireland, in 2004 and 2006, respectively, and the Ph.D. degree in electrical engineering from the University of California at Los Angeles (UCLA), in 2012. He is currently a Senior Staff Scientist with the Broadcom Corporation, Irvine, CA.

REFERENCES [1] N. Deferm and P. Reynaert, “A 120 GHz 10 Gb/s phase-modulating transmitter in 65 nm LP CMOS,” in IEEE Int. Solid-State Circuits Conf., Feb. 2011, pp. 290–292. [2] L. Zhou, C.-C. Wang, Z. Chen, and P. Heydari, “A -band CMOS receiver chipset for millimeter-wave radiometer systems,” IEEE J. SolidState Circuits, vol. 46, no. 2, pp. 378–391, Feb. 2011. [3] Y.-A. Li, M.-H. Hung, S.-J. Huang, and J. Lee, “A fully integrated 77 GHz FMCW radar system in 65 nm CMOS,” in IEEE Int. Solid-State Circuits Conf., Feb. 2010, pp. 216–217. [4] J. Y.-C. Liu, A. Tang, N.-Y. Wang, Q. J. Gu, R. Berenguer, H.-H. Hsieh, C. Jou, and M.-C. F. Chang, “A -band self-healing power amplifier with adaptive feedback bias control in 65 nm CMOS,” in IEEE RFIC Symp., Jun. 2011, pp. 1–4. [5] J. Y. C. Liu, Q. J. Gu, A. Tang, N.-Y. Wang, and M. C. Chang, “A 60 GHz tunable output profile power amplifier in 65 nm CMOS,” IEEE Microw. Wireless Compon. Lett., vol. 21, no. 7, pp. 377–379, Jul. 2011. [6] D. Murphy, Q. J. Gu, Y.-C. Wu, H.-Y. Jian, Z. Xu, A. Tang, F. Wang, and M.-C. F. Chang, “A low phase noise, wideband and compact CMOS PLL for use in a heterodyne 802.15.3c transceiver,” IEEE J. Solid-State Circuits, vol. 46, no. 7, pp. 1606–1617, Jul. 2011. [7] T. LaRocca, S. W. Tam, D. Huang, Q. Gu, W. Hant, and M. F. Chang, “Millimeter-Wave CMOS digital controlled artificial dielectric differential mode transmission lines for reconfigurable ICs,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 181–184. [8] S.-W. Tam, E. Socher, A. Wong, Y. Wang, L. D. Vu, and M.-C. F. Chang, “Simultaneous sub-harmonic injection-locked mm-wave frequency generators for multi-band communications in CMOS,” in IEEE RFIC Symp., Jun. 2008, pp. 131–134. [9] Z. Chen, C. Wang, and P. Heydari, “ -band frequency synthesis using -band PLL and two different frequency triplers,” in IEEE RFIC a Symp., Jun. 2011, pp. 1–4. [10] K. H. Tsai and S. I. Liu, “A 43.7 mW 96 GHz PLL in 65 nm CMOS,” in IEEE Int. Solid-State Circuits Conf., Feb. 2009, pp. 276–277. [11] Z. Xu, Q. Gu, Y. Wu, H. Jian, F. Wang, and F. Chang, “An integrated frequency synthesizer for 81–86 GHz satellite communication in 65 nm CMOS,” in IEEE RFIC Symp., May 2010, pp. 57–60. [12] A. Tang, D. Murphy, F. Hsiao, Q. Gu, Z. Xu, G. Virbila, Y. H. Wang, H. Wu, L. Nan, Y. Wu, and F. Chang, “A CMOS 135–150 GHz 0.4 dBm EIRP TX with 5.1 dB P1 dB extension using envelope feed-forward compensation,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [13] A. Tang, D. Murphy, G. Virbila, F. Hsiao, S.-W. Tam, H.-T. Yu, Y. Kim, A. Wong, A. Wong, Y.-C. Wu, and M.-C. F. Chang, “ -band frequency synthesis using a -band PLL and frequency tripler in 65 nm CMOS technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3.

Frank Hsiao is currently working toward the Ph.D. degree at the University of California, Los Angeles (UCLA). His research is focused on high-speed baseband signal processing, very large scale integration (VLSI), and mixed-signal integrated circuits design.

Gabriel Virbila is currently working toward the M.S. degree at the University of California at Los Angeles (UCLA).

Yen-Hsiang Wang (S’10) was born in Taipei, Taiwan, on February 16, 1986. He received the B.S. degree in electrical engineering from National Taiwan University (NTU), Taipei, Taiwan, in 2008, the M.S. degree in electrical engineering from the University of California at Los Angeles (UCLA), in 2011, and is currently working toward the Ph.D. degree at UCLA. His research focuses on the design of high-performance and low-power ADCs.

Hao Wu is currently working toward the Ph.D. degree at the University of California at Los Angeles (UCLA). His research concerns CMOS millimeter-wave circuit design for communication systems at 60 GHz and beyond.

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Yanghyo Kim is currently working toward the M.S. degree at the University of California at Los Angeles (UCLA).

Mau-Chung Frank Chang (F’96) is currently the Wintek Endowed Chair and Distinguished Professor of Electrical Engineering and the Chairman of the Electrical Engineering Department, University of California at Los Angeles (UCLA). Prior to joining UCLA, he was the Assistant Director and Department Manager of the High Speed Electronics Laboratory, Rockwell Science Center (1983–1997), Thousand Oaks, CA. During his tenure, he developed and transferred the Al–GaAs/GaAs heterojunction bipolar transistor (HBT) and BiFET (planar

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HBT/MESFET) integrated-circuit technologies from the research laboratory to the production line (now Conexant Systems and Skyworks Solutions). The HBT/BiFET productions have grown into multibillion-dollar businesses and dominated the cell-phone PA and front-end module markets (currently exceeding one billion units/year). Throughout his career, his research has primarily focused on the development of high-speed semiconductor devices and integrated circuits for RF and mixed-signal communication and imaging system applications. He was the Principal Investigator with the Rockwell Science Center, where he lead the Defense Advanced Research Project (DARPA)’s ultrahigh-speed ADC/DAC development for direct conversion transceiver (DCT) and digital radar receiver (DRR) systems. He invented the multiband reconfigurable RF interconnects based on FDMA and CDMA multiple access algorithms, for chip multiprocessor (CMP) inter-core communications and inter-chip CPU-to-memory communications. He also pioneered the development of the world’s first multigigabit/multiseccond ADC, DAC, and DDS in both GaAs HBT and Si CMOS technologies, the first 60-GHz radio transceiver front-end based on transformer-folded-cascode (Origami) high-linearity circuit topology, and the low phase-noise CMOS VCO F.O.M. dBc/Hz with digitally controlled on-chip artificial dielectric (DiCAD). Dr. Chang was elected to the U.S. National Academy of Engineering in 2008 for the development and commercialization of GaAs PAs and integrated circuits. He was the recipient of the 2006 IEEE David Sarnoff Award for the development and commercialization of HBT PAs for modern wireless communication systems.

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Generalization and Reduction of Line-Series-Shunt Calibration for Broadband GaAs and CMOS On-Wafer Scattering Parameter Measurements Chien-Chang Huang, Member, IEEE, and Yu-Chuan Chen

Abstract—This paper presents generalization and reduction of the line-series-shunt (LST) calibration technique, including generic parasitic treatments on the series/shunt standards and number reduction of calibration standards, for broadband GaAs and CMOS on-wafer scattering parameter ( -parameter) measurements. The series/shunt standards are modified with additional transmission-line (TL) sections on both the left and right sides to directly solve the five calibration parameters, namely, TL propagation constant, series impedance, shunt admittance, series parasitic admittance, and shunt parasitic impedance. This approach relaxes the constraint on the series/shunt standards that may not satisfy the plain lossy TL assumption in the parasitic evaluations. The calibration can be further reduced by only two standards if the lossy TL models for the series/shunt standards are satisfied. These points are examined by a microstrip test structure built on GaAs and CMOS technologies, with verification of an independent thru-reflect-line calibration. Index Terms—Calibrations, de-embedding, microwave measurement, on-wafer measurements, transmission-line (TL) elements.

I. INTRODUCTION

O

N-WAFER device characterization has a fundamental role in RFIC designs, where the scattering parameter ( -parameter) calibration and de-embedding are essential and important steps throughout the characterizing operation. Usually, the calibration initially utilizes the ceramic impedance-standard-substrate (ISS) [1] with line-reflect-match (LRM) or line-reflect-reflect-match (LRRM) calibration techniques [2] to shift the measured reference plane to the probe tips. Then, several dummy structures, such as open/short or two interconnect lines are provided to remove the parasitic effects associated with the device-under-test (DUT) [3]–[6]. The characterization accuracy, however, is highly dependent Manuscript received July 10, 2012; revised September 20, 2012; accepted September 24, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported in part by the National Science Council (NSC), Taiwan, under Grant NSC 100-2220-E-155-002 and Grant NSC 101-2220-E-155-001. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. C.-C. Huang is with the Department of Communication Engineering, Yuan Ze University, Taoyuan 320, Taiwan (e-mail: [email protected]). Y.-C. Chen was with the Department of Communication Engineering, Yuan Ze University, Taoyuan 320, Taiwan. He is now with Microelectronics Technology Incorporation, Hsinchu 8863, Taiwan. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222921

on how valid the parasitic circuit modeling is and how ideal the dummy structures are. There is an alternative approach with on-chip calibration standards, such as on-chip LRM/LRRM, that performs calibration and de-embedding on the same substrate without parasitic circuit modeling requirements. However, the load standard should be precisely characterized in advance. Though the multiline thru-reflect-line (TRL) calibration [7], [8] works well for on-wafer measurements, a larger chip area using two or more lines standards increases the test cost. A broadband line-series-shunt (LST) calibration method suitable for on-wafer calibration has been reported [9], where the characteristics of the calibration standards do not need to be known. The calibration accuracy, however, is highly dependent on the parasitic effects due to nonzero length of the series/shunt resistors. The parasitic elements cannot be determined directly through the LST self-calibration, and the lossy TL models are developed for GaAs devices to solve the problem [9]. However, for CMOS technologies, the thin-film resistor process is generally not available. The poly or bulk resistors placed under the metal layers introduce extra parasitic effects for which the plain lossy TL models for the CMOS resistors are inadequate. Clearly, more general solution schemes should be developed for the parasitic evaluations of the general series/shunt standards, thereby extending the applicability of the LST calibration to CMOS or any other technologies. Recently, a generalized solution scheme for the LST calibration technique was proposed [10] to show the capability of generic series/shunt parasitic evaluations. Five determining equations in the self-calibration procedure were acquired to solve the five unknown calibration parameters, including TL propagation constant, series impedance, shunt admittance, series parasitic admittance, and shunt parasitic impedance. The GaAs microstrip test structures with two thin-film resistors as series/shunt standards and a 0.15- m pseudomorphic high-electron mobility transistor (pHEMT) as DUT were examined to validate the proposed solution scheme [10], where the series/shunt standards satisfied the lossy TL models to verify the parasitic evaluation results by the direct solution approach. This paper extends the concept of [10] with additional TL sections on both sides of the series/shunt standards for more general LST calibration formulations to provide more design freedom of the calibration kit. In addition, the two determining equations generated by the asymmetric TL lengths of series/shunt standards can also yield the possibility of only two-standard calibrations, providing that the lossy TL models are valid for the series/

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admittance , and the parasitic elements and . We use five trace invariance equations of the actual cascading matrix , , manipulations in , , and with their corresponding measured cascading matrix manipulations as

(1a)

Fig. 1. Illustration of line, offset-series, and offset-shunt calibration standards with - and -network representations for series/shunt resistors.

(1b)

shunt standards. In this paper, we show that the reduced version of LST calibration in offset-series and offset-shunt combination gives comparable calibration accuracy as measured on GaAs devices. The measured results for GaAs and CMOS devices using various LST calibrations are provided from 2 to 50 GHz to show the different applicable conditions. The additional TRL calibration is performed also in the frequency range of 6–50 GHz to further verify the proposed calibration methods. II. GENERALIZATION OF LST CALIBRATION

(1c)

A. Self-Calibration Procedure The schematic diagrams of the three on-chip calibration standards, including line, offset-series, and offset-shunt, are shown in Fig. 1 with the associated probe transitions and interconnect TLs after the probe tips were calibrated by commercial ISS. The measurement system can then be modeled as the standards embedding two error boxes in cascading connection, (usually in 50 ). For referred to as the system impedance mathematical convenience, the cascading matrix [11] is used instead of -parameter in derivations. On the other hand, the series and shunt resistors are represented by the - and -netand can be treated as work, respectively, where parasitic elements due to nonzero lengths of resistors [9]. The - and -networks are further simplified to and since the resistors can be designed and fabricated in symmetry. If the symmetries of series/shunt standards are not satisfied, the solving parameters with the error boxes then will deviate a little. Fortunately, the parasitic effects can be made small by using small-dimension series/shunt resistors. As a result, the error due to the asymmetry can be reduced further. The self-calibration technique is applied based on the similarity transformation of the matrix multiplications between the actual and the measured cascading matrixes to determine the five unknown calibration parameters, including the TL propaga, the series impedance , the shunt tion constant

(1d)

(1e) All of the equations in (1) should be identically equal to zeros and repwhen the solutions are obtained. Note that resent the actual and the measured cascading matrixes, respectively. Subscripts , and , respectively, indicate the three calibration standards—line, offset-series, and offset-shunt. In addition, the subscript indicates the forward measurement from the left side as port 1 to the right side as port 2 of the standard device, while the subscript indicates the reverse measurement from the left as port 2 to the right as port 1 of the stan, dard device. Other variable definitions are listed as , , , , , and . In addition, is the characteristic impedance of the interconnect TL.

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OF

TABLE I THREE COMBINATIONS FOR TWO-STANDARD ON-WAFER CALIBRATIONS

Fig. 2. Microphotograph of three calibration standards and pHEMT DUT on GaAs substrate.

Compared with the determining equations of the LST calibration [9], (1d) and (1e) are the additional equations derived from the series/shunt offset TLs, which make the series/shunt standards asymmetrical. The solutions of the simultaneous nonlinear algebraic equations are acquired by the Newton–Raphson iteration process [9], while the Jacobian can be analytically derived from (1). The initial guesses for the calibration parameters are given as follows: from the empirical formula for the TL structure, from dc measurements, from the lossy . TL models [9], and Degeneracy can occur as the determining equations of (1) become trivial. Normally, it happens as the series impedance or the shunt admittance going to zero or infinity, or the line phase shift to make the equations in trivial. A good indication to show the ill-conditioned problem for the calibration is the condition number of the Jacobian of the determining equation (1). One can choose a set of calibration parameters and then check the condition number of the Jacobian through simulations in the design stage. B. De-Embedding Process Once the calibration parameters are known, the error boxes can be evaluated in an overdetermined sense by using five or fewer cascading matrix manipulations to solve the two

Fig. 3. Solved calibration parameters including (a) TL propagation constant, (b) series circuit elements, and (c) shunt circuit elements using three calibration methods for GaAs devices.

unknowns of the error boxes [9]. From our experience, the first three matrix manipulations are the optimum choice for stable solutions. Note that all of the calibration and the error box parameters are referred to as the TL characteristic impedance . The DUT -parameter referred to as is then acquired by de-embedding the solved error boxes. To convert the -parameter reference impedance to [9], the characteristic impedance must first be found. For this, it is evaluated with the TL unit-length capacitance at low substrate loss condition [9], [12], which may be achieved by careful design for TL structures with GaAs and CMOS technologies. The dc measured

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Fig. 4. Final de-embedded results of GaAs pHEMT DUT using four calibration methods with measured differences between TRL and L-OS-OT/LST/OS-OT calibration results for (a) input reflection, (b) forward transmission, (c) reverse transmission, and (d) output reflection.

resistances for the series/shunt standards are utilized, respectively, to determine the TL unit-length capacitance with the expressions (2a) (2b) and are the measured reflection coefficients where after calibration for the series and the shunt resistors, respectively. The low-frequency condition in (2) means that the resistor behaves like a lumped component in dc resistance [12]; it can be satisfied as long as the resistor electrical length is not greater than one degree. The characteristic impedance is calculated by , and the reference impedance of the DUT -parameter is transformed accordingly [9]. III. REDUCTION OF LST CALIBRATION If the lossy TL models are valid for the series/shunt standards, then the parasitic effects can be evaluated by explicit expressions accurately [9]. This case reduces the unknown number

of the calibration parameters to three, with only two-standard calibrations being possible. Having fewer standards is always attractive to save chip area and measurement time, providing that too much calibration accuracy is not sacrificed. There are three combinations, namely, line/offset-series, line/offset-shunt, and offset-series/offset-shunt, that can be used to perform the two-standard calibrations. They are described in detail below. The first case of line/offset-series combination with two unknowns of and utilizes the matrix manipulations of and to produce the determining equations of (1a) and (1d), respectively. On the other hand, the second case of line/offset-shunt combination has a mathematical structure similar to the first case, where the unknown is changed to and the determining equations of (1b) and (1e) derived from the matrix manipulations of and are used. The third case of offset-series/offset-shunt combination, however, like the LST calibration has three unknowns. We can choose the matrix manipulations of , and to provide the determining equations, namely, (1c), (1d) and (1e), to solve the calibration parameters as well. In fact, the offset-series/offset-shunt calibration can be seen as the line standard being embedded in the offset-series and offset-shunt standards so that the standalone line standard is

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Fig. 5. Microphotograph of three calibration standards and NMOSFET DUT on silicon substrate.

not required. The parasitic effects for the series/shunt resistors are evaluated based on the lossy TL models as [9] (3a) (3b) where and are the lengths of the series resistor and the shunt resistor, respectively. Though the above three combinations of calibration standards, at least in theory, can solve the unknown calibration parameters, the first two cases perform with high sensitivity for the solved results under measurement uncertainties. Fortunately, the offset-series/offset-shunt combination still provides acceptable numerical stability in practical operations as demonstrated in the next section. Note that the reverse transmission coefficient product of the error box -parameters in the LST de-embedding process is evaluated by using the line standard measured -parameter [9]. Thus it must be changed to the expressions with the offset-series measured -parameter or the offset-shunt measured -parameter as

Fig. 6. Solved calibration parameters including (a) TL propagation constant, (b) series circuit elements, and (c) shunt circuit elements using three calibration methods for CMOS devices.

(4a) IV. MEASUREMENT RESULTS A. GaAs Devices

(4b) Table I summarizes the calibration unknowns, matrix manipulations for solving, parasitic evaluations, and remark for the three combinations of two-standard on-wafer calibrations.

The calibration standards, including line, offset-series and offset-shunt with a two-finger pHEMT DUT in 0.15- m gate length and 100- m gate width, are fabricated on the GaAs substrate in 100- m thickness using microstrip structure, where the line lengths are 425 m, 375 m, 0 m, and 0 m with a line width of 72 m. The thin-film resistors are utilized for the series/shunt standards. The series resistor width is also 72 m and it is 30 m long, resulting in a 16- resistance. The shunt standard is implemented

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Fig. 7. Final de-embedded results of NMOSFET DUT using four calibration methods with measured differences between TRL and L-OS-OT/LST/OS-OT calibration results for (a) input reflection, (b) forward transmission, (c) reverse transmission, and (d) output reflection.

by two identical parallel resistors of 30 m along the line direction and 40 m long connected to ground, resulting in a 54resistance. The lossy TL models thus can be applied to compare the calibration results with the direct solving approach. The chip microphotograph is shown in Fig. 2. One should be noted that the large mismatch conditions for the calibration standards, including very large series impedance, very large shunt admittance, and very different impedance levels between the on-chip transmission line and the measurement system. All of the above cases may lead the ill-conditioned problem for the calibration and de-embedding. In our experiences, designs in the range of 10–200 for the series/shunt resistors are workable. The characteristic impedance of the on-chip transmission line is certainly designed to 50 as much as one can. The solved calibration parameters are shown in Fig. 3 from 2 to 50 GHz, where the imaginary part of the propagation constant is represented by the effective dielectric constant in the relation of and is the speed of light in vacuum. The data obtained by the proposed generalized method is designated as L-OS-OT to differentiate it from the plain LST calibration data. The solution results of the two-standard calibration using offset-series and offset-shunt, marked as OS-OT, are shown as well, and the three results show good agreement. The propagation constant is further verified by an independent

TRL calibration from 6 to 50 GHz to ensure the validity of the proposed calibration methods. The pHEMT DUT de-embedded results from 2 to 50 GHz are shown in Fig. 4 using the three calibration methods for comparison, where the pHEMT is biased at 0.4 V for and 3.0 V for . The additional TRL calibration results are also given from 6 to 50 GHz, where the measured differences with the three previous calibration methods are also indicated. It can be observed that the LST calibration with the lossy TL models for the series/shunt standards shows the data closest to the TRL calibration results. On the other hand, the de-embedded results using the L-OS-OT and the OS-OT calibration methods show a slight fluctuation through the frequency sweep. B. CMOS Devices The TL structure of the CMOS calibration standards should be designed in low substrate loss condition, as described in Section II-B. We can take advantages of the low loss features for the inter-metal dielectrics of the CMOS back-end process. In this study, the TSMC 0.18- m 1P6M technology is utilized, where metal-1 acts as the ground plane and metal-6 plays the role as the signal strip to constitute the thin-film microstrip TL. The line lengths are 720 m, 120 m, 0 m, 0 m with line width of 15 m. 103 m and Poly resistors are used for the series/shunt standards. The series

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resistor length is 7 m with the same width as the line width, resulting 159 in resistance. The shunt standard is implemented by two identical parallel resistors of 5 m along the line direction and 6 m long connected to a ground, resulting 340 in resistance. A chip microphotograph of the CMOS calibration standards is shown in Fig. 5. It should be noted that there are extra parasitic effects for the poly resistor rather than a plain lossy TL model as in the GaAs case since the poly resistor is placed below metal-1 and is connected to the signal strip in metal-6 by vias. Fig. 6 shows the solved calibration parameters using L-OS-OT, LST and OS-OT calibration methods from 2 to 50 GHz, with the TRL calibration results in TL propagation constant from 6 to 50 GHz for verification. The TL propagation constants obtained by the L-OS-OT and TRL methods agree well, but some discrepancies can be observed for LST and OS-OT results compared with TRL data, as shown in Fig. 6(a). This phenomenon is due to the extra parasitic effects for the series/shunt resistors, in which plain lossy TL models are invalid. The differences for the solved series/shunt parameters using L-OS-OT, LST and OS-OT methods are more obvious, especially for the series parasitic element , as shown in Fig. 6(b). The DUT of an 18-finger NMOSFET in 0.18- m gate length and 5- m gate width is examined using the above calibration methods, where the FET is biased at of 1.0 V and of 1.8 V. The de-embedded DUT S-parameters using L-OS-OT, LST and OS-OT calibration methods are shown in Fig. 7 in the frequency range of 2–50 GHz. The additional TRL calibration results from 6 to 50 GHz are also provided for verification where the measured differences between TRL and the three calibration methods (L-OS-OT, LST and OS-OT) are indicated, respectively. Again data using the L-OS-OT method are quite close to the TRL results, while the LST and OS-OT data show some deviations from the L-OS-OT/TRL results. In summary, unlike the GaAs measurement case, only the L-OS-OT calibration method is applicable for CMOS on-chip calibration applications. V. CONCLUSION This paper shows generalization and reduction of the LSTtype calibration techniques applied to GaAs and CMOS device de-embedding by using additional TL sections for the series and shunt standards, with verifications of the TRL calibration. This approach is important when the thin-film resistor is not available, such as with the CMOS process, since series and shunt resistors do not satisfy the plain lossy TL models. The paper also shows the availability of the two-standard calibration, providing the lossy TL models are valid for the series/shunt resistors. Throughout the measured results, the L-OS-OT calibration method can be applied to GaAs and CMOS device characterization applications, whereas the OS-OT method is suitable for GaAs technology with advantage of less calibration standards to save chip area and measurement time. More comprehensive statistical and sensitivity analyses for the calibrations will be conducted in the future. These calibration methods and measurement results will be useful for RFIC designs with various semiconductor technologies. ACKNOWLEDGMENT The authors would like to thank the Chip Implementation Center (CIC), Taiwan, for arranging the schedules of WIN

Semiconductors in pHEMT process and TSMC in CMOS process, and the Nano Device Laboratory (NDL), Taiwan, for support in measurements. REFERENCES [1] “Impedance standard substrate,” Cascade Microtech, Inc., Beaverton, OR. [Online]. Available: http://www.cmicro.com/products/calibration-tools [2] R. Davison, K. Jones, and E. Strid, “LRM and LRRM calibrations with automatics determinations of load inductance,” in Proc. 36th ARFTG Conf., Monterey, CA, 1990, pp. 84–91. [3] L. F. Tiemeijer, R. J. Havens, A. B. M. Jansman, and Y. Bouttement, “Comparison of the pad-open-short and open-short-load deembedding techniques for accurate on-wafer RF characterization of high-quality passives,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 2, pp. 723–729, Feb. 2005. [4] X. Wei, G. Niu, S. L. Sweeney, Q. Liang, X. Wang, and S. S. Taylor, “A general 4-port solution for 110 GHz on-wafer transistor measurements with or without impedance standard substrate (ISS) calibration,” IEEE Trans. Electron Devices, vol. 54, no. 10, pp. 2706–2714, Oct. 2007. [5] I. M. Kang, S.-J. Jung, T. H. Choi, J.-H. Jung, C. Chung, H.-S. Kim, H. Oh, H. W. Lee, G. Jo, Y.-K. Kim, H.-G. Kim, and K.-M. Choi, “Five step (pad-pad short-pad open-short-open) de-embedding method and its verification,” IEEE Electron Device Lett., vol. 30, no. 4, Apr. 2009. [6] H.-Y. Cho, J.-K. Huang, C.-K. Kuo, S. Liu, and C.-Y. Wu, “A novel transmission line deembedding technique for RF device characterization,” IEEE Trans. Electron Devices, vol. 56, no. 12, pp. 3160–3167, Dec. 2009. [7] R. B. Marks, “A multiline method of network analyzer calibration,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 7, pp. 1205–1215, Jul. 1991. [8] D. F. Williams, J. C. M. Wang, and U. Arz, “An optimal vector-network-analyzer calibration algorithm,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 12, pp. 2391–2401, Dec. 2003. [9] C.-C. Huang, Y.-H. Lin, and M.-Y. Chang-Chien, “Accuracy improvement for line-series-shunt calibration in broadband scattering parameter measurements with applications of on-wafer device characterization,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 9, pp. 2497–2503, Sep. 2010. [10] C.-C. Huang and Y.-C. Chen, “Generalized solving scheme of line-series-shunt type calibration for broadband on-wafer scattering parameter measurements,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [11] G. F. Engen, Microwave Circuit Theory and Foundations of Microwave Metrology. London, U.K.: Inst. Electr. Eng., 1992, pp. 25–26. [12] R. B. Marks and D. F. Williams, “Characteristic impedance determination using propagation constant measurement,” IEEE Microw. Guided Wave Lett., vol. 1, pp. 141–143, Jun. 1991.

Chien-Chang Huang (S’92–M’95) received the M.S. and Ph.D. degrees in electrical engineering from National Taiwan University, Taipei, Taiwan, in 1990 and 1994, respectively. From 1994 to 1996, he was an Associate Researcher with the Transmission Laboratory, Telecommunication Laboratories, Taoyuan, Taiwan, where he developed RF circuits and subsystems for personal communications systems. He is currently with the Department of Communication Engineering, Yuan Ze University, Taoyuan, Taiwan. His research interests include microwave device characterization and modeling, computer-aided analysis of RF/microwave circuits, and wireless communications.

Yu-Chuan Chen received the B.S. degree in electrical engineering and M.S. degree in communication engineering from Yuan Ze University, Taoyuan, Taiwan, in 2009 and 2011, respectively. He is currently with Microelectronics Technology Inc., Hsinchu, Taiwan. His research interests include high-power amplifier designs and microwave measurements.

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Experimental Characterization of Stability Margins in Microwave Amplifiers Nerea Otegi, Aitziber Anakabe, Joana Pelaz, Juan-Mari Collantes, and Geoffroy Soubercaze-Pun

Abstract—This paper proposes a method for the experimental estimation of the stability margins in microwave amplifiers. The approach is based on measuring a closed-loop frequency response representing the linearization of the circuit about a steady-state solution. Critical poles of the amplifier are then obtained by applying conventional pole-zero identification techniques to the measured frequency response. As circuit parameters are modified, the evolution of these critical poles on the complex plane provides a practical way to assess the robustness of the design regarding its stability. Two types of common instabilities in microwave amplifiers are studied: low-frequency bias oscillations and parametric oscillations. For the low-frequency oscillations, the approach proposes the inclusion of an observation RF port into the amplifier bias path to experimentally obtain the critical poles of the circuit from a reflection coefficient measurement. Pole-placement techniques are then applied to increase the stability margin of detected critical resonances. For the parametric oscillations, pole-zero identification is applied to a frequency response obtained from a mixer-like characterization equivalent to the measurement of a “hot” reflection coefficient. The methodology is applied to two amplifier prototypes: an -band field-effect transistor amplifier and a dual-mode WiFi-WIMAX amplifier that exhibit different kinds of unstable behavior. Index Terms—Circuit stability, identification, measurement, poles and zeros, stabilization networks.

I. INTRODUCTION

R

OBUST DESIGN of microwave amplifiers in terms of circuit stability implies the lack of undesired autonomous frequency components for operating conditions that can be very far from nominal. This means that an originally stable design must not exhibit undesired oscillations due to aging, technological dispersion or operating condition variations (such as temperature, bias, load, or even the mounting setup). However, microwave amplifiers are prone to exhibit spurious oscillations of Manuscript received July 10, 2012; revised September 19, 2012; accepted September 20, 2012. This work was supported in part by Spanish and Basque administrations, respectively, under Project TEC2009-09874 and Project IT456-10. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. N. Otegi, A. Anakabe, J. Pelaz, and J.-M. Collantes are with the Departamento de Electricidad y Electrónica, University of the Basque Country (UPV/EHU), Bilbao 48080, Spain (e-mail: [email protected]; [email protected]; [email protected]; [email protected]); G. Soubercaze-Pun is with the Centre National d’Etudes Spatiales (CNES), Toulouse Space Centre, 31401 Toulouse, France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2221736

different nature and at different frequencies due to the large band gain of microwave transistors and their intrinsic nonlinear behavior [1], [2]. To analyze the robustness of a design with respect to spurious oscillations, local stability analyses at simulation level can be performed. Different methods are available for both smallsignal [3]–[7] and large-signal [1], [2], [8]–[16] regimes. Stability margins with respect to relevant circuit parameters can be estimated from parametric or Monte Carlo stability simulations [2], [3], [17], [18]. However, for that to be effective, accurate nonlinear models of the active devices are needed, as well as a fine and accurate description (including electro-thermal) of all the circuit elements and circuit environment. Unfortunately, reliable models and fine circuit descriptions are not always available, and in this case, simulation is not an option for the assessment of the stability margins. In addition, power spectrum measurements of a stable amplifier do not provide relevant information about the possible critical resonances that can lead to an unstable behavior when some conditions change, unless we are near to the bifurcation point and a noise bump is observable in the spectrum [2], [18], [19]. In [20], a procedure has been presented in order to experimentally determine and control the critical low-frequency poles of a microwave amplifier. Although stable, these critical poles have small real parts and they may lead to instability when operating and/or environment conditions are changed. The procedure is based on adding an extra RF port in series with an RC stabilization network connected to the amplifier bias path in order to monitor and control the low-frequency dynamics. In this paper, the work in [20] has been extended in two ways. First, the validity of the approach to detect and control critical poles of oscillations associated to the bias circuitry has been proven at higher frequencies. In these kind of oscillations, the elements of the bias networks combine with the intrinsic feedback elements of the active device (generally a gate-to-drain or a base-to-collector capacitance) to satisfy the oscillation conditions as in a Hartley topology [21]. These oscillations start up from a dc regime that is set by the bias point and can happen from a few kilohertz to hundreds of megahertz, depending on the amplifier. In this work, it will be evidenced that pole placement techniques based on root contour tracing are reliable at least up to hundreds of megahertz. Therefore, using root contours we can get a consistent estimation of the values of the stabilization elements that increase the stability margins and diminish the risk of spurious oscillations versus changes in amplifier conditions. Second, the approach has been generalized to the detection of critical poles on large-signal steady states, as in the case of parametric spurious oscillations or parametric frequency divisions.

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Fig. 1. Third port introduced in series with an RC bias stabilization network for the purpose of measuring and controlling critical poles of a two-port amplifier. Under test mode, the third port is connected to a VNA. Under normal operation mode the third port is short circuited.

These oscillations depend on the power level and the fundamental frequency of the input drive. They can have their origin in the negative resistance generated by a nonlinear capacitance pumped by the large-signal input drive [2]. In this case, critical poles will be extracted from a single reflection measurement carried out in a mixer like characterization setup. This paper is organized as follows. Section II presents the method to access the low-frequency dynamics of the amplifier and the pole placement strategies that allow an increase of the stability margins with respect to the stabilization elements. The experimental validation on an -band field-effect transistor (FET) amplifier prototype with critical resonances between 100–200 MHz is shown in Section III. The extension to parametric oscillations on large-signal regimes is addressed in Section IV. A dual-mode WiFi-WIMAX amplifier prototype that exhibits parametric frequency division and autonomous spurious is used to experimentally illustrate the approach. II. OBSERVATION PORT FOR THE LOW-FREQUENCY DYNAMICS Critical low-frequency resonances have been measured using low-frequency coaxial probes in [22]. Here, we adopt the technique proposed in [20], in which an RF observation port is added to the amplifier at a certain node of the gate bias path (Fig. 1). This port is connected in series to a stabilization RC network. This kind of stabilization network is typically inserted in power amplifiers to improve stability at low frequencies [23], [24]. The circuit now has two operating modes depending on what is connected to this third port: a normal operating mode if a short circuit is connected to the port and a test mode with a vector network analyzer (VNA) connected at the port. With the circuit in test mode, the reflection coefficient at the observation port is measured. is then converted to the admittance frequency response as (1) being 50 . Fig. 2 compares the meaning of in test with and normal operation modes. In test mode, is the admittance

Fig. 2. Comparison of the meaning of in: (a) test mode and (b) normal obtained in test mode is equivalent to mode. The frequency response obtained by an ideal voltage source connected in series at the third the port for a stability analysis of the normal operation mode.

that the amplifier presents to the VNA [see Fig. 2(a)]. In addition, is also the admittance seen by an ideal voltage source connected in series at port 3 [see Fig. 2(b)]. In fact, the schematic of Fig. 2(b) corresponds to a conventional stability analysis of the normal operation mode in which pole-zero identification of the frequency response provides the poles of the circuit linearized around its dc solution [7]. Therefore, the key point of the approach is that, in test mode, we are able to measure a valid frequency response for pole-zero identification of the circuit operating in normal mode. Obviously, the former is true provided that the dc solution does not change from normal to test mode. This is guaranteed by the presence of the stabilization capacitor in the RC network that is in series with the observation port. Adding the third RF port to the amplifier has two main benefits for circuit diagnosis. • First, its inclusion in the bias path provides an observation port with high sensitivity to the low-frequency dynamics. This is very important because low-frequency resonances are almost unobservable from input and output RF ports of the amplifier due to the isolating effect of the matching networks. This isolation results in very tiny resonances that can be masked by the measurement noise and are impossible to identify. • Second, the two elements of the stabilization network ( and ) can be directly related to the proportional and integral control actions of a generic control scheme [7]. Actually, as shown in Fig. 3, a variation of the series stabilization resistance is equivalent to a proportional control action, applied on the feedback path, over the original admittance function [see Fig. 2(b)]. The value of this variation is directly the proportional constant of the control action (2)

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Fig. 3. Variation of the series stabilization resistance: proportional control acobtained with and . tion over the original admittance function

3

Fig. 4. Variation of the series stabilization capacitance: integral control action obtained with and . over the original admittance function

so that the closed-loop transfer function resulting from the application of a proportional control action is given by (3) Similarly, as shown in Fig. 4, variations of the original series stabilization capacitance are equivalent to an integral control action over the original admittance function , applied on the feedback path. Here, the capacitance added in series with the original stabilization capacitance is the inverse of the integral control constant (4) In this way, the closed-loop transfer function resulting from the application of an integral control action is given by (5)

Therefore, once the circuit poles have been detected , these equivalences allow the automatic esfrom timation of the pole evolution on the complex plane when the two stabilization parameters are modified. This can be easily done by tracing root locus for proportional control or root contour for integral control [25], [26]. As a result, we can determine from a single measurement the values of and that improve the stability margin by pushing leftward the circuit poles. III. EXPERIMENTAL CONTROL OF LOW-FREQUENCY RESONANCES IN AN FET AMPLIFIER In this section we present an application example of the proposed method. Low-frequency critical poles of a single stage -band FET (FLU17XM) amplifier are measured and

Fig. 5. Photograph of the amplifier, including the third port and the RC stabilization network, and basic block diagram of the measurement setup in test mode.

controlled. Fig. 5 shows a photograph of the amplifier and the measurement setup for the test mode operation. The port for the observation of the low-frequency dynamics (port 3) is implemented in the gate bias path, in series with the RC stabilization network. Nominal values for the stabilization parameters are and pF. An E5061 VNA is connected at port 3 to measure the reflection coefficient . The frequency response is then computed from (1). It is worthwhile to point out that is measured at the input of the RC stabilization network (included as part of the amplifier in Fig. 5), according to the analysis developed in Section II. An E4440A spectrum analyzer (SA) is connected to the output port of the amplifier (port 2) in order to verify that the circuit is not oscillating in test mode. It is important to note that measurement noise is a critical aspect in frequency-domain identification because it can hide parts of the system dynamics or aggravate overmodeling problems [27], [28]. Therefore, in our setup, measurement noise has to be minimized as much as possible because an identification of will follow up. Thus, very narrow IF filtering and high averaging are used for the reflection measurement in the VNA, resulting in a rather slow characterization process. In normal operation mode (short circuit at port 3), the amplifier in Fig. 5 exhibits an oscillation at around 110 MHz [see Fig. 6(a)] for nominal bias conditions V

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Fig. 6. Output spectrum for V and V measured in: (a) normal operation mode (port 3 short circuited) and (b) test mode (port 3 connected to VNA).

Fig. 8. Identification results of for ciated pole-zero map ( : poles, ο: zeros).

V and

V: asso-

Fig. 7. Identification results of for V and V: Magnitude and phase of the measured (crosses) and identified (solid line) frequency responses.

V . However, in test mode (the VNA loading port 3), the amplifier is stable, as shown in the spectrum of Fig. 6(b). This gives us the possibility to measure and obtain the frequency response in these conditions. Results are plotted with crosses in Fig. 7. Three clear resonances are observed at around 110, 170, and 200 MHz. Next, system identification is applied to to get the associated pole-zero map of Fig. 8. We can observe in Fig. 7 that, in spite of the measurement noise, identification of (solid line) provides an excellent fit of the measured values (crosses). The pole-zero map of Fig. 8 shows a couple of unstable complex conjugate poles at 110 MHz, in agreement with the oscillation observed in Fig. 6(a). It is important to remember that the frequency response obtained in test mode (circuit stable) provides the poles of the circuit corresponding to normal operation mode (unstable in this case). That is why unstable poles can actually be measured in this circuit. Apart from these unstable poles, complex conjugate poles associated to the resonances at 170 and 200 MHz are also present in the pole-zero map. Once the pole-zero map has been obtained from , we can proceed to trace the root contours to estimate the evolution of the circuit poles on the complex plane versus variations of

Fig. 9. Direct proportional control action over : predicted evolution of critical poles versus the value of the stabilization resistance.

the stabilization parameters. Automatic routines for root locus tracing are available in most common packages for mathematical computing [29], [30]. The root locus plot corresponding to a proportional control action is shown in Fig. 9. For sake of clarity, only positive frequencies of the complex plane are plotted in Fig. 9. Note that the evolution parameter in the plot is not the proportional parameter , but the total equivalent resistance required in the RC stabilization network to get the same control effect, i.e., (6) which is more practical from the design point of view. The plot shows that a stabilization resistor in the interval 29 69 is able to stabilize the amplifier. This is consistent with the fact that the amplifier is stable in test mode, with the VNA connected at port 3. Assuming that the VNA presents 50 , its connection at port 3 is equivalent to a of 52 , which is inside the stable interval. At higher values of the circuit becomes unstable again. This is expected because of the presence of the complex

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Fig. 10. Direct (solid line) and inverse (dashed line) integral control action over : predicted evolution of critical poles versus the value of the stabilization capacitance.

conjugate pair of zeros lying on the right half-plane (RHP), close to the unstable poles. The proportional action departs from the pole and ends at the zero nearby, which makes it very difficult to stabilize. In conclusion, proportional control is not a robust solution for the stabilization of this particular example. Next, root contour for integral control has been traced in Fig. 10. Direct and inverse controls are plotted in solid and dashed lines, respectively. Since , direct integral control corresponds to decreasing positive values of . In turn, inverse integral control implies negative values of decreasing magnitude. Again, for convenience, the evolution parameter depicted in the root contours of Fig. 10 is the total equivalent capacitance of the stabilization network resulting from the series connection of and (Fig. 4) (7)

since this is the parameter that the designer can manipulate in practice. Fig. 10 shows that a direct integral control does not stabilize the system (solid line in Fig. 10). For the resonances at 110 and 170 MHz, the pole evolution departs from the original pole location and ends at the zero nearby. Therefore, the unstable 110-MHz poles remain on the RHP. This is an expected result since direct integral control implies reducing the capacitance value of the RC stabilization network. On the contrary, inverse integral control (dashed line in Fig. 10) is able to place the three pairs of critical poles on the left half-plane (LHP). As the stabilization capacitance is increased, the 110-MHz poles move leftward and become stable for pF. At the same time, poles at 170 MHz shift down in frequency and move rightward, although they never become unstable. In turn, poles at 200 MHz evolve very quickly toward the zero nearby so that they stay in the stable region. Note that the inverse integral contours depart from the original pole location (corresponding to , ) and end at , . Values of are not traced in the

Fig. 11. Intervals of variation of the poles due to a 10 values: pF and pF. two

5

tolerance of

for

inverse integral control locus since they would imply nonfeasible negative values of . We can observe in the inverse integral contour of Fig. 10 that the pole evolution converges toward a fixed position on the LHP as is increased. In fact, for pF, the poles lie practically in the same location. A tolerance analysis has been combined to the pole evolution of Fig. 10. For the analysis, two capacitance values that stabilize the amplifier have been selected: pF and pF. 10 tolerances have then been assigned to these values. In Fig. 11, the intervals of variation of the corresponding poles due to these tolerances are represented. As it can be seen, pF does not guarantee a sufficient stability margin since the pole at 110 MHz dangerously approaches to the imaginary axis. In contrast, the location of the poles is not significantly affected by the tolerance in the pF case. This kind of analysis can serve to select the minimum capacitance value that guarantees reasonable stability margins. This can be useful in power amplifiers with dynamic supply architectures, such as envelope tracking amplifiers, where large low-frequency bypass capacitors are not recommended [31]. To verify the accuracy of the estimations predicted by the root contours, we have physically mounted different discrete values of stabilization capacitors in the RC stabilization network. The resulting critical poles have then been measured and are superimposed to the inverse integral control plot in Fig. 12. Results show a very good agreement with the predictions of Fig. 10, which confirms that the root contour tracing can be successfully extended at least up to a few hundreds of megahertz (note that, in [20], this was demonstrated up to 20 MHz only). In conclusion, root contour tracing from a single admittance measurement provides a reliable method to estimate the stability margins of the critical poles when the stabilization parameters and are varied. To support the interest of the third port for the observation of low-frequency dynamics, the admittance obtained from reflection-coefficient measurements at port 1 is shown in Fig. 13. No resonances are observable in Fig. 13, confirming that low-frequency resonances are generally undetectable from

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Fig. 14. Stability analysis of a large-signal periodic regime by means of the in order to obtain a introduction of a small-signal current source at node . closed-loop frequency response

Fig. 12. Evolution of critical poles of versus the stabilization capacitance. measured Dashed line: predicted by the integral control action over a single pF. Superimposed (symbols): measured poles correwith in the circuit. sponding to the mounting of different discrete values of

Fig. 15. Stability analysis of a large-signal periodic regime by means of the in order to obtain a introduction of a small-signal voltage source at branch . closed-loop frequency response

A. Mixer-Like Measurements

Fig. 13. Magnitude and phase of the frequency response port.

obtained at input

the RF access ports due to the isolating effect of the matching networks. As a result, the inclusion of the proposed observation port is indispensable to access the low-frequency dynamics experimentally. Its implementation in early prototype stages of a new design can provide valuable information to reduce the risk of low-frequency oscillations in final amplifier realizations. IV. EXTENSION TO THE CHARACTERIZATION OF CRITICAL RESONANCES IN LARGE-SIGNAL REGIMES In this section, experimental detection of critical resonances is extended to large-signal regimes. The approach needs substantial modifications from the previous small-signal analysis because of the periodic linear time variant (PLTV) nature of the system resulting from the linearization of a periodic large-signal regime. In addition, root locus tracing is not applicable in this context because of the intrinsic multiple-input/multiple-output nature of the PLTV systems [32].

The stability of a PLTV system is determined by its Floquet multipliers, which are the eigenvalues of the monodromial matrix [2]. In [33] and [34], it was demonstrated that associated Floquet exponents agree with the poles of the PLTV transfer function that linearly relates an arbitrary input at a perturbation frequency to an arbitrary output at with being the frequency of the large-signal pump and being the harmonic index, . In practice, since all the harmonic components of the PLTV transfer function share the same denominator, except for exact pole-zero cancellations, the system poles are usually determined from the first term of the harmonic series [35]. This kind of stability analysis is very common in simulation of microwave circuits, where the system poles are normally obtained from the identification of a simulated closed-loop frequency response [2], [12], [36]. This closed-loop response can be the total impedance seen by a small-signal current probe at connected in parallel at a particular circuit node , as depicted in Fig. 14, or the total admittance seen by a small-signal voltage probe at inserted in series at a certain branch (Fig. 15). Either or are obtained by performing a mixer-like simulation in which the input drive at plays the role of the local oscillator and the small-signal perturbation at represents the RF

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Fig. 16. Schematic of a generic circuit in which with a pump at port 1.

is measured at port

signal. This numerical simulation can make use of the system conversion matrix, actual linearization of the periodic regime, or a conventional two-tone harmonic-balance (HB) algorithm, with one of the two fundamentals of very small amplitude. In an experimental characterization, the linearization of the periodic large-signal regime can also be performed by measuring the frequency dependence of a reflection coefficient while the circuit is pumped by the input drive. This is equivalent to the measurement of a hot scattering parameter [37], [38] or to the measurement of the reflection coefficients at RF or IF ports in a mixer characterization [39]. Fig. 16 shows the schematic of a generic circuit in which a reflection coefficient is measured at port with a pump at port 1. From , we can calculate the impedance presented at that port (8) Then, analogously to Fig. 14, the total impedance presented to an ideal current probe connected in parallel at port would be (9) Similarly, as in Fig. 15, the total admittance seen by an ideal voltage probe connected in series at port can be computed as (10) Both and share the same denominator and both are valid closed-loop frequency responses for stability analysis of a large-signal periodic steady state. Pole-zero identification can be applied to or in order to get the poles of the linearized circuit, that is to say, in order to get the Floquet exponents of the PLTV system. Hot -parameters have been used for large-signal stability diagnosis in [37] and [38]. Compared to these studies, the application of pole-zero identification to (9) or (10) has the advantage of only needing the measurement of a single hot reflection coefficient. In addition, with the proposed approach, the system poles associated to critical resonances can be obtained. The evolution of these critical poles provides an estimation of the stability margin of the circuit. Three important considerations concerning the experimental approach have to be outlined.

7

• Linearization of a periodic large-signal regime depends upon the circuit terminations at and with . On the one hand, source and load terminations at influence the periodic large-signal steady state to be linearized. On the other hand, the resulting PLTV system is a function of the termination conditions at perturbation frequency and intermodulation products . This means that the closed-loop frequency responses and obtained as indicated in Fig. 16 from (9) and (10) are dependent on and . Any change in these termination conditions will imply a different linearized system. As a consequence, the terminations set by the characterization setup have to be fully consistent with the actual operation of the device-under-test (DUT). • The large-signal at that pumps the circuit must not saturate the VNA dedicated to the measurement of the hot reflection coefficient at . This should not be a problem for perturbation frequencies that are reasonably far from the pump frequency because, in the worst case, appropriate filtering can be used. • A key point in the linearization process is that the amplitude level of the perturbation, i.e., the power level at the VNA test port , has to be low enough to guarantee linear behavior of the system versus the perturbation. This is a requirement easy to fulfill in simulation. If conversion matrix is used, linearity with respect to the perturbation is guaranteed by definition. If two-tone HB is used instead, we can set the perturbation amplitude to very small value and still have enough numerical precision in the simulation. However, in a characterization process, the linearity requirement may imply a scattering measurement performed at very low test port power. This can compromise the accuracy of the results due to measurement noise. It is thus very important to use a VNA with the highest sensitivity setup as possible, although this will result in a slow measurement. These three points are important for the accuracy of the experimental results and have been carefully accounted for in Section IV-B where an experimental example of the methodology is given. B. Experimental Example The experimental example is a prototype of reconfigurable amplifier for WiFi/WiMAX applications (2.4/3.5 GHz), fabricated in microstrip hybrid technology with an SiGe BFP650 transistor (Fig. 17). Reconfigurability is achieved by means of two parallel input matching networks that will be externally switched by a single-pole double-throw switch. Thus, the prototype has two separate inputs, one tuned to 2.4 GHz and the other to 3.5 GHz. In normal operation mode, the input that is not being pumped is charged with an open circuit. When driven from the 3.5-GHz input, the prototype presents two different parametric instabilities versus input power at 3.5 GHz . As is increased, a parametric frequency division by 2 or an autonomous spurious (close to the divided frequency) appears in the output spectrum depending on the bias conditions. These undesired parametric oscillations

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Fig. 17. WiFi/WiMAX reconfigurable amplifier prototype built in microstrip hybrid technology. Fig. 19. Comparison of the responses corresponding to dBm input drive measured with five different settings: 40, 35, 30, 20, and 10 dBm.

Fig. 18. Schematic of the measurement setup: pumping signal ( at GHz) from a signal generator and test power ( at ) from the PNA are combined to the 3.5-GHz input; output port is connected to an SA and the 2.4-GHz input is open circuited.

are due to the negative resistance generated by a nonlinear capacitance pumped by the large-signal input drive, which also resonates with an inductive element close to the sub-harmonic frequency [2]. Fig. 18 shows a schematic of the measurement setup. A 11667A power combiner at the 3.5-GHz input port serves to apply the input drive at GHz from a signal generator while reflection measurements are carried out with a performance network analyzer PNA E8358A at port 1. The effect of the combiner has been de-embedded in the power results. The PNA provides the required performances in terms of sensitivity and dynamic range for this challenging measurement. Actually, it allows scattering parameter measurements with very low test port power levels (down to 90 dBm). A spectrum analyzer is connected to the output port of the amplifier to monitorize the output spectrum all along the measurement process. The reflection coefficient measurements at port 1, , are performed in the frequency interval GHz to capture the circuit dynamics at frequencies around . The total closed-loop admittance is then computed from , as in (8) and (10). will be used

for pole-zero identification instead of because it provides a better sensitivity in this particular example [40]. Let us review here, in the context of this particular example, the three important considerations outlined in Section IV-A. • The measurement setup of Fig. 18 determines the load conditions presented to the DUT during the characterization process. Being connected to the PNA and SA, respectively, a matched load condition can be considered for port 1 and port 3 at fundamental frequency and its harmonics , and intermodulation products . Similarly, open-circuit termination at port 2 is also broadband and it applies to all the relevant frequencies . As stated before, different load conditions (at and/or ) will derive in a different PLTV system. • The accuracy of the PNA measurements in the interval 1.6 1.9 GHz in the presence of a large-signal pump at 3.5 GHz has been verified through the measurements of passive standards as different power values at 3.5 GHz were applied. No saturation of the PNA receiver due to the 3.5-GHz signal pump was observed. Note that the isolation of the combiner is not critical since the frequency of the large signal pump is well outside the measurement frequency range. • The test port power of the PNA, , which ensures linear behavior of the DUT with respect to the perturbation, has been determined. For that, several responses obtained for different values are compared in Fig. 19. All these responses are measured with an input drive dBm at 3.5 GHz and with the amplifier biased at : mA, V. We can observe that test port power levels down to 30 dBm are required to get an that is independent of the power level. This emphasizes the need of using a VNA

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Fig. 20. Critical pole evolution for : the amplifier biased at

ranging from 8.2 to 10.1 dBm with mA, V.

Fig. 21. Power spectrum for dBm with the amplifier biased at : (a) 0.5–7.5-GHz frequency range and (b) 1.7–1.8-GHz frequency range. GHz. Periodic steady state at

with high sensitivity and with measurement capabilities at very low test port power levels. Having these considerations into account, pole-zero identification has been applied to frequency responses obtained for different values of . is maintained at 40 dBm in all the measurements. Fig. 20 shows the critical pole evolution obtained for ranging from 8.2 to 10.1 dBm, with the amplifier biased at . Only positive frequencies of the complex plane are plotted for the sake of simplicity. We can observe how two pairs of complex conjugate poles tend to collide at the divided frequency GHz as increases. After that, one pair shifts leftward, while the other moves rightward with increasing . This pole evolution is very typical in Flip bifurcations [2]. Identification of the last measurement point dBm is more problematic because of the effect of noise precursors, as according to the power spectrums shown below. We have measured the output power spectrum corresponding to several values. Complete spectra and zooms around the divided frequency are plotted in Figs. 21–23. Fig. 21 shows the power spectrum for dBm. The amplifier is perfectly stable and there is no evidence of risk of frequency division in spite of the fact that critical poles are already detected. However, for dBm, the power spectrum of Fig. 22 shows a characteristic noise precursor at , clearly depicted in the zoom of Fig. 22(b). This precursor has a disturbing effect on the measured frequency response. As a consequence, the obtained poles for dBm start to lose

9

Fig. 22. Power spectrum for dBm with the amplifier biased : (a) 0.5–7.5-GHz frequency range and (b) 1.7–1.8-GHz frequency range. at GHz with noise precursor around . Periodic steady state at

Fig. 23. Power spectrum for dBm with the amplifier biased : (a) 0.5–7.5-GHz frequency range and (b) 1.7–1.8-GHz frequency range. at GHz). Frequency-divided steady state (

Fig. 24. Critical pole evolution for : mA, amplifier biased at

ranging from 8 to 8.5 dBm with the V.

consistency with the pole evolution obtained for lower powers (Fig. 20). Finally, the power spectrum for dBm is plotted in Fig. 23. The frequency division by 2 is now clearly noticeable. The pole evolution versus obtained for a bias point : mA, V, is shown in Fig. 24. Again, only positive frequencies of the complex plane are plotted for the sake of clarity. In these conditions, the two pairs of complex conjugate poles shift rightward with increasing , but they do not collide in the LHP. They would do it in the RHP, although this cannot be obtained experimentally because this situation is not physically observable. This pole evolution predicts the show up of an autonomous component close to the divided frequency, together with a mixing product, for higher than 8.5 dBm.

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Fig. 25. Power spectrum for dBm with the amplifier biased at : (a) 0.5–7.5-GHz frequency range and (b) 1.5–2-GHz frequency range. Periodic GHz. steady state at

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ponent and the corresponding mixing term in the neighborhood of (Fig. 27). To our knowledge, this is the first time that this kind of pole evolutions showing the path toward a parametric instability are experimentally obtained in a microwave circuit. However, it is important to remark that, contrarily to the dc stability analysis, in large signal it is almost impossible to insert specific observation ports without modifying the steady state under analysis. Therefore, the success in the identification results depends on the accessibility to the critical circuit dynamics from its input and output RF ports. This can be a challenge in multistage power-combined structures that are prone to exhibit odd-mode parametric frequency division by 2. Ideally, no odd-mode dynamics can be observable from the input and output ports. In practice, a certain degree of observability can be expected due to the asymmetries in the architecture originated by the technological dispersion. This results in very tiny resonances, whose identification can be very challenging in the presence of measurement noise. V. CONCLUSION

Fig. 26. Power spectrum for dBm with the amplifier biased : (a) 0.5–7.5-GHz frequency range and (b) 1.5–2-GHz frequency range. at GHz with two noise precursors around . Periodic steady state at

An experimental methodology for evaluating the stability margins of microwave amplifiers with respect to different types of instabilities has been proposed. Low-frequency critical poles are extracted thanks to an additional RF port inserted in the bias path, in series with an RC stabilization network. It has been experimentally demonstrated that the pole evolution versus RC values can be truthfully predicted by applying pole-placement techniques to a single measurement performed at nominal RC values. Pole evolutions associated to autonomous and frequency-division parametric instabilities have also been obtained experimentally. To our knowledge, this is the first time that this kind of pole evolution is plotted from measurement data. The proposed approach can be useful, in the context of circuit diagnosis, helping in the understanding of the nonlinear behavior of a circuit, whenever this behavior cannot be predicted in simulation because of the limited accuracy of nonlinear models and/or circuit description. REFERENCES

Fig. 27. Power spectrum for dBm with the amplifier biased : (a) 0.5–7.5-GHz frequency range and (b) 1.5–2-GHz frequency range. at Quasi-periodic steady state with autonomous spurious around GHz .

The behavior expected from Fig. 24 is confirmed in Figs. 25–27 where the output spectra for several increasing values of are plotted. Again, a zoom around the divided frequency is also depicted in all cases. For dBm, the amplifier is stable, without evidence of risk of oscillation (Fig. 25). For dBm, two noise precursors around are shown in Fig. 26. Again, this situation corresponds to the nearest poles to the imaginary axis in Fig. 24. The effect of the noise precursors affects the measured frequency response. As a result, identification results lose consistency and a nonphysical third pair of poles is found for dBm, as shown in Fig. 24. Eventually, for dBm, the system is unstable, with the appearance of an autonomous com-

[1] A. Suarez and R. Quere, Stability Analysis of Nonlinear Microwave Circuits. Boston, MA: Artech House, 2003. [2] A. Suarez, Analysis and Design of Autonomous Microwave Circuits. New York: Wiley, 2009. [3] F. Centurelli, G. Scotti, P. Tommasino, and A. Trifiletti, “A synthesisoriented approach to design microwave multidevice amplifiers with a prefixed stability margin,” IEEE Microw. Guided Wave Lett., vol. 10, no. 3, pp. 102–104, Mar. 2000. [4] R. G. Freitag, “A unified analysis of MMIC power amplifier stability,” in IEEE MTT-S Int. Microw. Symp. Dig., Albuquerque, NM, Jun. 1992, vol. 1, pp. 297–300. [5] A. Costantini, G. Vannini, F. Filicori, and A. Santarelli, “Stability analysis of multi-transistor microwave power amplifiers,” in Gallium Arsenide Appl. Symp. Tech. Dig., Paris, France, Oct. 2000, pp. 342–345. [6] W. Struble and A. Platzker, “A rigorous yet simple method for determining stability of linear n-port networks,” in 15th Gallium Arsenide Integr. Circuit Symp. Tech. Dig., Oct. 1993, pp. 251–254. [7] N. Ayllon, J. M. Collantes, A. Anakabe, I. Lizarraga, G. SoubercazePun, and S. Forestier, “Systematic approach to the stabilization of multitransistor circuits,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 8, pp. 2073–2082, Aug. 2011. [8] V. Rizzoli and A. Lipparini, “General stability analysis of periodic steady-state regimes in nonlinear microwave circuits,” IEEE Trans. Microw. Theory Techn., vol. MTT-33, no. 1, pp. 30–37, Jan. 1985.

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[9] A. Suarez, S. Jeon, and D. Rutledge, “Stability analysis and stabilization of power amplifiers,” IEEE Microw. Mag., vol. 7, no. 5, pp. 51–65, Oct. 2006. [10] A. Suarez, J. Morales, and R. Quere, “Chaos prediction in an MMIC frequency divider in millimetric band,” IEEE Microw. Guided Wave Lett., vol. 8, no. 1, pp. 21–23, Jan. 1998. [11] S. Mons, J. C. Nallatamby, R. Quere, P. Savary, and J. Obregon, “A unified approach for the linear and nonlinear stability analysis of microwave circuits using commercially available tools,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 12, pp. 2403–2409, Dec. 1999. [12] J. Jugo, J. Portilla, A. Anakabe, A. Suarez, and J. M. Collantes, “Closed-loop stability analysis of microwave amplifiers,” Electron. Lett., vol. 37, no. 4, pp. 226–228, Feb. 2001. [13] P. Bolcato, J. C. Nallatamby, C. Rumolo, R. Larchevêque, M. Prigent, and J. Obregon, “Efficient algorithm for steady-state stability analysis of large Analog/RF circuits,” in IEEE MTT-S Int. Microw. Symp. Dig., Phoenix, AZ, May 2001, vol. 1, pp. 451–454. [14] C. Barquinero, A. Suarez, A. Herrera, and J. L. García, “Complete stability analysis of multifunction MMIC circuits,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 10, pp. 2024–2033, Oct. 2007. [15] L. Pantoli, G. Leuzzi, A. Santarelli, F. Filicori, and R. Giofre, “Stabilisation approach for multi-device parallel power amplifiers under large-signal regime,” in 6th Eur. Microw. Integr. Circuits Conf., Manchester, U.K., Oct. 2011, pp. 144–147. [16] F. Cappelluti, F. L. Traversa, F. Bonani, S. D. Guerrieri, and G. Ghione, “Rigorous, HB-based nonlinear stability analysis of multi-device power amplifier,” in 40th Eur. Microw. Conf., Paris, France, Sep. 2010, pp. 90–93. [17] J. M. Collantes, N. Otegi, A. Anakabe, N. Ayllon, A. Mallet, and G. Soubercaze-Pun, “Monte-Carlo stability analysis of microwave amplifiers,” in 12th Annu. IEEE Wireless Microw. Technol. Conf., Clearwater Beach, FL, Apr. 2011, pp. 1–6. [18] S. Jeon, A. Suarez, and D. B. Rutledge, “Analysis and elimination of hysteresis and noisy precursors in power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 3, pp. 1096–1106, Mar. 2006. [19] J. Jeffries and K. Wiesenfeld, “Observation of noisy precursors of dynamical instabilities,” Phys. Rev. A, Gen. Phys., vol. 31, no. 2, pp. 1077–1084, Feb. 1985. [20] N. Otegi, A. Anakabe, J. Pelaz, J. M. Collantes, and G. SoubercazePun, “Increasing low-frequency stability margins in microwave amplifiers from experimental data,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [21] G. Gonzalez, Foundations of Oscillator Circuit Design. Boston, MA: Artech House, 2006. [22] S. Rumery and B. Noori, “A new technique for measuring the resonant behaviour of power amplifier bias circuits,” in 69th ARFTG Conf., Honolulu, HI, Jun. 2007, pp. 1–9. [23] R. Basset, “High-power GaAs FET device bias considerations,” Fujitsu, San Jose, CA, Fujitsu Appl. Note 010, 2008. [24] C. M. Olsen, S. L. Sweeney, and K. A. Remley, “Representing bias-network baseband characteristics when simulating intermodulation distortion,” in 76th ARFTG Microw. Meas. Symp., Clearwater Beach, FL, Nov. 2010, pp. 1–6. [25] G. F. Frankiln, J. D. Powell, and A. Emani-Naeini, Feedback Control of Dynamic Systems. Reading, MA: Addison-Wesley, 1994. [26] G. C. Goodwin, S. F. Graebe, and M. E. Salgado, Control System Design. Upper Saddle River, NJ: Prentice-Hall, 2001. [27] R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach. New York: Wiley, 2001. [28] A. Anakabe, N. Ayllon, J. M. Collantes, A. Mallet, G. Soubercaze-Pun, and K. Narendra, “Automatic pole-zero identification for multivariable large-signal stability analysis of RF and microwave circuits,” in 40th Eur. Microw. Conf., Paris, France, Sep. 2010, pp. 477–480. [29] Scilab. Scilab Enterprises, Orsay Cedex, France, 2012. [Online]. Available: http://www.scilab.org [30] MATLAB. The MathWorks Inc., Natick, MA, 2012. [Online]. Available: http://www.mathworks.com/products/matlab [31] E. McCune, “Envelope tracking or polar—Which is it?,” IEEE Microw. Mag., vol. 13, no. 4, pp. 34–56, Jun. 2012. [32] E. Möllerstedt and B. Bernhardsson, “Out of control because the harmonics—An analysis of the harmonic response of an inverter locomotive,” IEEE Control Syst. Mag., vol. 20, no. 4, pp. 70–81, Aug. 2000.

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[33] J. Roychowdhury, “Reduced-order modelling of linear time-varying systems,” in Proc. IEEE/ACM Int. Comput.-Aided Design Conf., Nov. 1998, pp. 92–95. [34] F. Bonani and M. Gilli, “Analysis of stability and bifurcations of limit cycles in Chuas’s circuit through the harmonic-balance approach,” IEEE Trans. Circuits Syst. I, Fund. Theory Appl., vol. 46, no. 8, pp. 881–890, Aug. 1999. [35] J. M. Collantes, I. Lizarraga, A. Anakabe, and J. Jugo, “Stability verification of microwave circuits through Floquet multiplier analysis,” in IEEE APCCAS, Tainan, Taiwan, Dec. 2004, pp. 997–1000. [36] Y. Butel, D. Langrez, J. F. Villemazet, G. Coury, J. Decroix, and J. L. Cazaux, “Low cost MMIC chipset for VSAT ground terminals,” in Eur. Microw. Conf., Oct. 2005, vol. 3, pp. 1–4. [37] T. Gasseling, D. Barataud, S. Mons, J. M. Nebus, J. P. Villotte, J. Obregon, and R. Quere, “Hot small-signal -parameter measurements of power transistors operation under large-signal conditions in a loadpull environment for the study of nonlinear parametric interactions,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 3, pp. 805–812, Mar. 2004. [38] “Hot S22 and hot -factor measurements,” Anritsu, Morgan Hill, CA, Appl. Note AN11410-00295, Aug. 2002. [39] “RF component measurements-mixer measurements using the 8753B network analyzer,” Agilent Technol., Santa Clara, CA, Agilent Product Note PN 8753-2, 2000. [40] N. Ayllon, A. Anakabe, J. M. Collantes, G. Soubercaze-Pun, and S. Forestier, “Sensitivity enhancement in pole-zero identification based stability analysis of microwave circuits,” in Integr. Nonlinear Microw. Millim.-Wave Circuits Workshop, Malaga, Spain, Nov. 2008, pp. 75–78. Nerea Otegi received the Ph.D. degree from the University of the Basque Country (UPV/EHU), Bilbao, Spain, in 2008. In 2002, she joined the Departamento de Electricidad y Electrónica, UPV/EHU, where she has been an Associate Professor since 2006. Her areas of interest include noise characterization at microwave frequencies and nonlinear analysis of microwave circuits.

Aitziber Anakabe received the Ph.D. degree in electronics from the University of the Basque Country (UPV/EHU), Bilbao, Spain, in 2004. In 1999, she joined the Departamento de Electricidad y Electrónica, UPV/EHU, where she was involved with the stability analysis of nonlinear microwave circuits. In 2004, she joined the French Space Agency (CNES), Toulouse, France, as a Post-Doctoral Researcher. In 2005, she rejoined the Departamento de Electricidad y Electrónica, UPV/EHU, where, since 2005, she has been an Associate Professor. Her research concerns nonlinear analysis and modeling of microwave circuits and measurement techniques.

Joana Pelaz was born in Barakaldo, Spain, on August 9, 1987. She received the M.Sc. degree in electronics engineering from the University of the Basque Country (UPV/EHU), Bilbao, Spain, in 2010, and is currently working toward the Ph.D. degree in linear and nonlinear stability analysis of microwave active circuits at UPV/EHU. She is currently with the Departamento de Electricidad y Electrónica, UPV/EHU. Her main research interests include analysis and design of microwave circuits and linear and nonlinear experimental characterization.

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Juan-Mari Collantes received the Ph.D. degree in electronics from the University of Limoges, Limoges, France, in 1996. Since February 1996, he has been an Associate Professor with the Departamento de Electricidad y Electrónica, University of the Basque Country (UPV/EHU), Bilbao, Spain. In 1996 and 1998, he was an Invited Researcher with Agilent Technologies (formerly the Hewlett-Packard Company), Santa Rosa, CA. In 2003, he was with the French Space Agency (CNES), Toulouse, France, where he was involved with power amplifier analysis, simulation, and modeling. His areas of interest include nonlinear analysis and design of microwave circuits, microwave measurement techniques, and noise characterization.

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Geoffroy Soubercaze-Pun received the Ph.D. degree in electronics from the University of Toulouse, Toulouse, France, in 2007. He was initially with Thales Alenia Space France, where he was involved with frequency synthesis. In 2008, he joined the French Space Agency (CNES), Toulouse, France. His main research interests are power amplifiers and nonlinear analysis of microwave circuits.

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A 1–8-GHz Miniaturized Spectroscopy System for Permittivity Detection and Mixture Characterization of Organic Chemicals Ahmed A. Helmy, Student Member, IEEE, and Kamran Entesari, Member, IEEE

Abstract—In this paper, a miniaturized broadband dielectric spectroscopy system is presented for permittivity detection, chemical sensing, and mixture characterization for 1–8-GHz frequency range. A sensing capacitor exposed to the material under test (MUT) is part of a true time-delay (TTD) cell excited by a microwave signal at the sensing frequency of interest. The phase shift of the microwave signal at the output of the TTD cell compared to its input is a measure of the permittivity of MUTs. For wideband and accurate sensing, TTD cells are cascaded in a reconfigurable fashion to increase the detected phase shift, especially at low frequencies. TTD cells are designed to detect permittivities within the range of 1–30 considering nonideal effects, such as electromagnetic coupling between adjacent TTD cells. Calibration using reference liquids is applied to the fabricated sensor and sensor characteristics are extracted. Permittivity detection of organic chemicals is performed in the range of 1–8 GHz with an error less than 2%. The measured permittivities in the 1–8-GHz range are used to estimate the sub-1-GHz permittivities of MUTs using extrapolation. The sensing system is also used for mixture characterization to find the mixing ratios in binary mixtures with an accuracy of 1%. Index Terms—Chemical sensor, dielectric constant, permittivity detection, spectroscopy, true time delay (TTD), mixture characterization.

I. INTRODUCTION

S

ENSING dielectric properties of chemicals and biochemicals is useful for a variety of applications, including drug and food safety, disease diagnosis, medical instrumentation, gas detection, alarm sensing, material characterization, and oil exploration and processing [1]–[5]. Dielectric sensing can also be used to study and improve the quality of agricultural products using soil and leaf characterization [6], [7]. Sensing dielectric properties of chemicals/biochemicals at microwave frequencies is quite relevant because: 1) important information regarding chemical structure and composition of chemicals/biochemicals at the microwave frequency range will be revealed [1]; 2) health hazards and nonthermal effects Manuscript received July 09, 2012; revised September 25, 2012; accepted September 27, 2012. Date of publication November 20, 2012; date of current version December 13, 2012. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 USA (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2224363

caused by microwave signals used in wireless communications on food and drug safety and on biochemicals inside living organisms, such as the human blood, will be investigated [2]; 3) microwave dielectric characterization of chemicals/biochemicals can be used for medical diagnosis; the dielectric properties of biomaterials such as blood [2], [3], semen [4], and cerebra spinal fluid [5] in patients with specific diseases are different compared to healthy people at microwave frequencies; one example is blood sugar control for diabetics by monitoring the glucose concentration inside the human blood [8], [9]; and 4) knowledge of electromagnetic (EM) properties of chemicals and biochemicals, including their dielectric properties, is an essential part of developing microwave medical techniques, such as thermography and tomography [10]. The need for broadband microwave dielectric spectroscopy is also quite relevant because: 1) the above mentioned applications for microwave dielectric measurements can be applied for a wider range of frequencies; this can help in studying interactions of materials with signals in a wider frequency range for more accurate characterization; 2) many materials may share the same value of the permittivity at a single frequency; therefore, detecting the unique frequency dispersive characteristics [11] of the material under test (MUT) over a wide frequency range is useful for more accurate material detection; and 3) low-frequency techniques for zero-frequency permittivity detection of ionic liquids fail due to high electrical conductance of these liquids at low frequencies [12]. However, the dielectric properties of these liquids can be easily extracted at microwave frequencies, and then they can be extrapolated to obtain the static dielectric constant [12]. One main goal in sensor design is the self-sustainability that aims to perform the complete sensing operation in a standalone fashion using elements integrated on board without the need of any external equipment. Self-sustained systems are necessary for portable sensors targeting many applications, including biological and medical sensors, such as portable and body implanted blood sugar control devices. Dielectric detection techniques are classified into frequency- and time-domain techniques. Many frequency-domain techniques for dielectric detection are based on microwave resonators [8], [13], where the permittivity detection is due to the change of the resonance frequency and the quality factor of the resonator when the MUT is applied. This technique is narrowband and cannot be applied for broadband microwave dielectric spectroscopy. Reported broadband spectroscopy sensors are based on measuring the magnitude and phase of the

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scattering matrix parameters of a transmission line or a coaxial probe exposed to the MUT [14]–[16], which are then used to estimate the permittivity of the MUT over a wide frequency range. Planar miniaturized techniques based on substrate integrated waveguide resonators and planar microstrip resonators are also employed for low-cost wideband miniaturized permittivity detection with moderate accuracy compared to resonator-based sensors [17]–[19]. Reported frequency-domain techniques [14]–[19] are employing vector network analyzers (VNAs) to measure the scattering parameters of the sensor for permittivity detection. This technique enables high detection accuracy by taking advantage of highly precise commercial and bulky VNAs. The time-domain dielectric spectroscopy (TDDS) technique is based on measuring the reflection of a fast rising step voltage applied to a transmission line terminated by the sample subject to characterization [20]–[22]. Compared to frequency-domain spectroscopy techniques, time-domain spectroscopy has the advantage of capturing the frequency-domain characteristics of the sample under test at once using a single step voltage generator followed by applying mathematical time to frequency signal conversion, such as Fourier transform, thus eliminating the need of a wideband frequency synthesizer. However, reported time-domain spectroscopy techniques are associated with bulky step voltage generators and digital oscilloscopes [21] or bulky time-domain reflectometers (TDRs) [22]. To the best knowledge of the authors, all reported frequencyand time-domain spectroscopy techniques are not suitable for self-sustained operation due to the need for bulky and expensive measurement equipment, such as VNAs, scopes, and TDRs. Accordingly, reported techniques are not suitable for portable and implanted sensors. This paper presents a novel low-cost compact size broadband dielectric spectroscopy system for the frequency range of 1–8 GHz [23]. The sensor employs a sensing capacitor as a part of a broadband true time-delay (TTD) cell. The sensing capacitor is exposed to the MUT, and as a result the capacitance and the phase of the signal passing through the TTD cell change as a function of the permittivity of the MUT. This phase shift is measured using on-board phase detectors working based on the principle of correlation. Compared to reported broadband frequency-domain dielectric spectroscopy techniques [14]–[19], the proposed technique employs simple lumped passive elements operating as TTD elements that can be easily miniaturized and reconfigured for a wide frequency range operation with high accuracy. The implementation of the proposed sensor is considered as the first step toward a self-sustained miniaturized dielectric spectroscopy system since no external VNA, TDR, or scope are used for detection purposes. However, as a proof of concept, the microwave signal applied to the TTD cells is generated using an external microwave signal generator, which can be replaced by on-board miniaturized discrete frequency synthesizers for a fully self-sustained system. In this study, the real part of the permittivity of the MUT is detected. Since materials have different frequency dispersion characteristics over a broad frequency range [11], the detection of over wide range of frequencies (1–8 GHz) is enough to

Fig. 1. (a) Electrical model of the sensing capacitor when exposed to MUT. (b) Sensing capacitor embedded inside the TTD cell.

distinguish among MUTs without extraction of their loss properties. Section II discusses the sensing cell analysis, design, and simulations. It also discusses design considerations of cascaded sensing units including EM coupling between adjacent TTD cells, design methodology of cascaded cells, and fabricated prototype characterization. The system implementation is presented in Section III. Circuit implementation and test setup for chemicals are described in Section IV. Section V shows the detailed experimental procedures and results for sensor calibration and dielectric spectroscopy of organic chemicals in the frequency range of 1–8 GHz for different sample volumes. Section VI presents applications to dielectric characterization and spectroscopy including the estimation of the static permittivity using extrapolation and the mixture characterization. Finally, Section VII concludes this paper. II. BASIC IDEA AND SENSING CELL DESIGN A. Sensing Cell Design The relative permittivity of any material is a frequency dependent complex quantity given by [11]. Accordingly, a capacitor exposed to a MUT and excited by a signal at a certain frequency can be used to detect the complex permittivity of this material at the excitation frequency. A sensing capacitor can be modeled as a capacitance in parallel with a resistor. When exposed to air ( and ), the sensing element is ideally modeled as a capacitance of with an infinite parallel resistance. When exposed to the MUT , the capacitor’s model changes to a capacitance of in parallel with a resistance of , as shown in Fig. 1(a). The value of the capacitance changes proportional to the real part of the permittivity independent of the material’s loss. The increase of material’s loss, or the imaginary part of the permittivity, results in lower resistance in parallel, thus degrading the quality factor of the sensing capacitor. In order to detect the change in the sensing capacitance for a wide frequency range, the capacitor is embedded inside a TTD cell, as shown in Fig. 1(b). The TTD cell is a low-pass LC T-network that can provide a phase shift up to 90 [24]. The change of the capacitance is translated into a change in the phase shift of the microwave signal passing through the TTD cell, which is used to estimate of the MUT, as will be explained later. The TTD cell elements should be designed for broadband input/output matching for wideband spectroscopy purpose. The TTD cell is firstly assumed to be a T-network composed of two inductors and a high

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Fig. 2. Layout of the sensing capacitor on Rogers Duroid 5880. (a) Top view. (b) Cross-sectional view.

quality factor sensing capacitance with an infinite sensing resistance . The two-port -parameters of this network with respect to a characteristic impedance of are proved to be given by [24] (1) (2) (3) (4)

Fig. 3. EM simulations of the sensing capacitor at 1, 4, and 8 GHz. (a) Sensing versus . (b) Quality factor of the sensing capacitor capacitance . versus

where (5) Using (1) and (4), the condition for perfect input/output matching is given by (6) Accordingly, the perfect broadband matching condition in (6) is frequency independent for (7) where . However, for broadband matching better than 10 dB, and using (1), (4), and (7), the matching condition is given by (8) The frequency-dependent phase shift of the signal passing through the TTD cell is the phase of . Using (3) and considering the broadband matching condition in (7), the phase shift of the TTD cell is given by (9) Accordingly, the change of the capacitance upon exposure to the MUT is translated into a change of the phase shift of the microwave signal passing through the TTD cell if the matching condition is satisfied.

Fig. 2 shows the implementation of the sensing capacitor on a Rogers Duroid 5880 substrate ( and mm). The sensing capacitor is implemented using a pair of metal lines on the top metal layer with the ground plane removed under the sensing capacitor to reduce the parasitic capacitance, as shown in Fig. 2. The sensing capacitor is simulated using Sonnet.1 The values of the capacitance and quality factor of the sensing capacitor versus and are shown in Fig. 3(a) and (b), respectively, for different frequencies. In this simulation, the permittivities are assumed frequency independent for simplicity. Fig. 3(a) shows that the capacitance increases with from 40 fF to around 300 fF for permittivities ranging from 1 to 30 at different frequencies (1, 4, and 8 GHz). The simulation was performed for different values of and the value of the sensing capacitance was proved to be independent of material’s loss at all frequencies. Fig. 3(b) shows that the quality factor of the sensing capacitor decreases with the increase of the material’s loss. From Fig. 3(a), the wide variation of the sensing capacitance can be noticed. This is to cover a wide range of . Based on (1), large values of , corresponding to larger values of , may affect the input/output impedance matching. This results in reflections in the TTD cell leading to phase-shift errors and then degrading the detection accuracy. One way to compensate for the effect of increasing on the value of is to increase the value of without compromising the sensitivity of 1Sonnet

Inc., North Syracuse, NY. [Online]. Available: www.sonnet.com

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Fig. 4. Schematic of the TTD cell with fixed capacitor sensing capacitor.

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in series with the

the sensing capacitor to MUTs. However, based on (1) and (7), increasing both and decreases the upper limit of frequency at which the matching condition is satisfied. One other way is to use a smaller sensing capacitor to limit the variations of the capacitance and prevent mismatch. However, smaller sensing capacitors results in harder manipulation of the tubes containing the liquids under characterization on top of the sensing for elements, as will be shown later. Accordingly, to prevent mismatches, a fixed capacitor is added in series with , as shown in Fig. 4, to suppress the wide variations of at the cost of the sensitivity reduction without decreasing the sensing capacitor. For a fixed capacitance of fF, the values of combined series capacitance of and versus are shown in Fig. 5(a) and are limited to values between 30–100 fF. The sensitivity of the capacitance to the permittivity of MUTs is defined as the ratio between the change of capacitance and the change of the permittivity ( . The addition of the series fixed capacitor degrades the sensitivity from 8.6 to 2.4 fF, but with the advantage of keeping broadband input matching. The degradation of the sensitivity is compensated by cascading multiple TTD cells, as will be shown later. Assuming that the fixed capacitor has a very high quality factor , then the overall quality factor of the series combination of the sensing and fixed capacitors is proved to be given by

Fig. 5. Effect of adding a fixed capacitor in series with the sensing capacitor. at 1, 4, and 8 GHz. (b) Effective quality (a) Effective capacitance versus versus for values of and . factor

(10) versus for different Fig. 5(b) shows the values of values of . The effective quality factor of the series combination of and is always higher than . Therefore, the addition of a series fixed capacitor reduces the wide variations of the sensing capacitance for broadband matching [see Fig. 5(a)], but desensitize the loss effect of the sensing capacitor. Accordingly, the performance of the TTD cell is expected to be independent of , as will be shown later. For wideband impedance matching better than 10 dB up to an 8-GHz frequency range, conditions in (7) and (8) should be satisfied. Accordingly, the values of TTD cell elements are chosen to be nH, 40 fF fF, and fF satisfying the condition for input matching better than 10 dB in (8) and the wideband input matching condition in (7). The TTD cell is implemented on a Rogers substrate, as shown in Fig. 6, with a total area of 2 3 mm . The planar inductor is implemented using a meander line and the fixed capacitor is

Fig. 6. Layout of the basic TTD cell on Rogers Duroid 5880 substrate with a total area of 2 3 mm . (a) 3-D view. (b) Top view. (c) A–A cross-sectional side view. (d) B–B cross-sectional side view. Drawing is not to scale.

implemented as a vertical parallel-plate capacitor between the top and bottom layers of the substrate. The capacitance of the sensing capacitor can be evaluated using the partial capacitance technique along with conformal mapping techniques evaluating the total capacitance between two sets of fingers in multilayered structures [25], [26]. The inductance of meander line inductors is based on the segmentation of the meander line into several straight lines. The overall inductance of the meander line is the resultant of the self-inductance effects of each straight line along with the mutual inductance effect between lines, as

HELMY AND ENTESARI: 1–8-GHz MINIATURIZED SPECTROSCOPY SYSTEM FOR PERMITTIVITY DETECTION AND MIXTURE CHARACTERIZATION

Fig. 8. Layout of three TTD cells with a center-to-center distance of MUT on top of the sensing capacitor.

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and

phase shift generated by a single broadband TTD cell is not enough for accurate detection for a wide frequency range. To improve the detection accuracy, the overall phase shift may be increased by cascading multiple TTD cells. Assuming broadband input/output impedance matching for each TTD cell, the phase shift resulting from cascading -TTD cells is approximately given by the phase shift of one cell multiplied by Fig. 7. Simulations of the TTD cell when exposed to materials with permitin decibels. (b) tivity range of 1–30 and loss tangent range of 0–1. (a) and in decibels.

reported in [27]. The TTD cell is simulated using Sonnet with materials having permittivities within the range of 1–30 and loss tangents within the range of 0–1. Fig. 7(a) shows that the return loss is better than 12 dB over the 1–8-GHz frequency range for two different materials ( ; and ). Fig. 7(b) shows the magnitude and phase of of the TTD cell. The phase of reflects the amount of phase shift generated by the TTD cell. The phase shift increases with both frequency and . For the same value of , the simulation is performed for different values of and proved no phase-shift dependency on the material’s loss. Fig. 7(b) on the right axis shows the insertion loss is less than 0.07 and 0.4 dB for materials with , ; and , ; respectively, for the 1–8-GHz frequency range. Accordingly, the TTD cell can detect independent of the material’s loss. B. Cascaded TTD Cells As shown in Fig. 7, the phase shift of the microwave signal passing through the TTD cell increases with the sensing frequency and permittivity . For example, at 1 GHz, the phase shift changes from 1.5 to 3.3 , whereas, at 8 GHz, the phase shift changes from 11 to 22 when changes from 1 to 30. The change of phase shift will be detected using a correlator whose output is the cosine of the phase shift, as will be explained later. Accordingly, the low values of phase shift, especially at lower frequencies, results in poor detection accuracy. Therefore, the

(11) The phase shift in (11) is valid assuming no EM coupling between different TTD cells. However, placing the TTD cells next to each other for miniaturization and exposing them to MUTs provides EM coupling among different TTD cells through the deposited material. As a result, the phase shift in (11) is not an accurate measure of the real phase shift. For simplicity, the EM coupling effect on one arbitrary cell is assumed to be only from the closest preceding and following stages and the effect of faraway cells is ignored. Fig. 8 shows the layout of three adjacent cascaded TTD cells with the liquid deposited on top of the sensing capacitors to study the coupling effect of cells 1 and 3 on cell 2. The length of the TTD cell, or the center-to-center distance between TTD cells, is given by . Using EM simulation, the phase shift of a microwave signal passing through three TTD cells in Fig. 8 is simulated and swept versus frequency for different values of and different materials, as shown in Fig. 9(a) and (b). The simulated phase shifts for different values of are compared to the ideal phase shift , where . Increasing the separation between the TTD cells is expected to decrease the EM coupling effect, and therefore, the simulated phase shift approaches the ideal response. Increasing above 2 mm results in minor change in the phase response of the three TTD cells compared to the ideal response at the cost of an increase of the sensor’s area. Therefore, a value of mm is chosen as the center-to-center distance between TTD cells. As mentioned before, the output of the correlator used for detection is the cosine of the phase shift of the microwave signal passing through -TTD cascaded cells. The phase shift should be limited to values between 0 –90 to prevent any

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Fig. 10. Simulated phase response versus frequency for different sub-fre. quency ranges

Fig. 9. Simulated phase response of three cascaded TTD cells for different with the ideal response defined as , where values of , for two values of permittivity, (a) , , (b) , .

phase ambiguity due to the cosine function. As the phase shift across one TTD cell varies with frequency [see Fig. 7(b)], the assigned number of cascaded TTD cells should also vary with the sensing frequency to avoid ambiguity. In other words, the phase shift is measured across a larger number of TTD cells for lower frequencies. Based on the phase-shift values in Fig. 7(b), the sensing frequency range of 1–8 GHz is divided into sub-frequency ranges and the number of cascaded TTD cells varies according to each range. The th frequency range covers the range between and with cascaded TTD cells. In this range, the minimum phase shift is and the maximum phase shift is . For a given , the value of is selected such that to achieve the best accuracy without phase ambiguity. For example, for 1–8-GHz frequency range, if the maximum value of is arbitrarily selected to be 14 , then the first sub-frequency range is chosen such that GHz (minimum frequency) and , which occurs at GHz, as shown in Fig. 7(b). Higher sub-frequency ranges are chosen such that and .A similar procedure is repeated to cover the entire range from 1 to 8 GHz.

Fig. 11. Prototype of 14 TTD cells in cascade fabricated using Rogers Duroid , , and mm). 5880 substrates (

Assuming that arbitrarily drops by 2 from one sub-frequency to another for and GHz GHz, the frequency range is divided into six bands, as shown in Fig. 10. For proof of concept, simple prototypes are fabricated using a Rogers Duroid 5880 substrate with the TTD cell described above. Each prototype is composed of -TTD cells in cascade with and , and center-to-center separation of 2 mm. Fig. 11 shows the photograph of one of the prototypes with . Fig. 12(a) shows an input matching better than 10 dB for the 14 TTD cells in cascade when exposed to air ( and for all frequencies) and methanol whose permittivity is frequency dependent and follows the Cole–Cole model given in [11]. The insertion loss and phase shift are measured across each prototype in the corresponding sub-frequency range specified in Fig. 10. For example, the detection in 4.3–5.9-GHz frequency range is performed using the prototype composed of six cascaded TTD cells. Fig. 12(b) shows the insertion loss for air and methanol for different values of corresponding to different sub-frequency ranges. This measurement proves insertion loss less than 0.3 and 0.8 dB, for air and methanol; respectively, for the entire frequency range, which corresponds to values of loss less than 0.07 and 0.2 dB for a single TTD cell. These results mean that the effect of lossy materials, such as methanol [11], on the insertion loss of the TTD cell is minimal. Accordingly, the output of the correlator is less sensitive to loss properties and the real part of the permittivity can be detected with enough accuracy. Moreover, one way to minimize the effect of the amplitude

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Fig. 12. (a) Measured return loss and (b) measured insertion loss of the prototypes when air and methanol are deposited.

variation due to material’s loss on the output of the correlator is proposed in [28]. This circuit can be added to the system by applying the output of the TTD cell to a voltage limiter, or to a high-gain amplifier to saturate the amplitude level of the signal at the input of the correlator. Accordingly, the output of the correlator is less dependent on the amplitude variation due to material’s loss in case a higher detection accuracy of is needed with highly loss materials. Fig. 13 shows the measurements of the phase shift compared to EM simulations considering the frequency dependency of of deposited materials. The EM simulation is performed separately for each frequency considering the corresponding value of of air and methanol from the Cole–Cole model in the simulation. Fig. 13(a) and (b) shows the simulated and measured phase response of different prototypes when exposed to air and methanol, respectively, proving the proper operation of cascaded TTD cells. In this system, the frequency range is limited to 1–8 GHz. However, the proposed system and techniques are still valid for chemical detection at frequencies higher than 8 GHz. This requires extending the frequency range at which acceptable input matching is still achieved, as given in (7) and (8). The upper frequency limit can be increased above 8 GHz by decreasing the value of the TTD cell elements in Fig. 4, including the sensing capacitor, to make the input matching condition less sensitive to any capacitance variation due to permittivity of MUTs. However, this comes at the cost of lower phase shift and sensitivity,

Fig. 13. Simulated and measured phase shift of the prototypes when: (a) air and (b) methanol are deposited.

Fig. 14. (a) -cascaded TTD cells with the input and output signals applied to a correlator. (b) Functional block diagram of the correlator.

especially at lower frequencies. Moreover, the lower frequency limit can be decreased by employing a greater number of TTD cells in cascade for higher detection accuracy at low frequencies at the cost of a larger sensor area. III. SYSTEM IMPLEMENTATION In order to detect the phase shift of a microwave signal passing through the chain of -cascaded TTD cells, the input and output signals are applied to a correlator, as shown in Fig. 14(a). The correlator consists of a down-conversion mixer

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Fig. 15. Reconfigurable sensing system by switching the input to the correlator.

applied

followed by a low-pass filter (LPF), as shown in Fig. 14(b). In Fig. 14, is a single-tone signal at the sensing frequency with an amplitude of , or . is a phase-shifted version of with an amplitude of , or , where is the phase shift achieved by - cascaded TTD cells and is approximately equal to times the phase shift achieved by one TTD cell . According to the EM simulations shown in Fig. 7(b), the TTD cell exhibits very low loss over the entire frequency range. Therefore, as a first-order approximation, the amplitudes of and are assumed to be equal . Accordingly, the output of the down-conversion mixer in Fig. 14(b) is the product of and and is given by

(12) If the cutoff frequency of the LPF following the mixer is much lower than , then the output of the correlator is a dc signal given by (13) Therefore, the dc output of the correlator is proportional to the cosine of the phase shift through -cascaded TTD cells and can be used to detect the permittivity in the corresponding frequency range. However, based on the analysis performed in Section II-B, the number of TTD cells assigned for permittivity detection is made frequency dependent for good detection accuracy (see Fig. 10). Therefore, the signals at the input of the correlator and should be reconfigured such that the number of TTD cells allocated between the input signals varies according to the the sub-frequency range (Fig. 10). This can be simply performed by switching the location of the second input of the correlator in a chain of cascaded TTD cells, as shown in Fig. 15. The system shown in Fig. 15 has two major practical issues, which are: 1) the correlator should be wideband covering the frequency range of 1–8 GHz; this can be alleviated by employing two or more correlators, each covering a portion of

the 1–8-GHz frequency range and 2) commercial microwave mixers have both inputs matched to low input impedance (around 50 ). Therefore, using a correlator to detect the phase shift between two points ( and ) on a single chain of -cascaded TTD cells (Fig. 15) loads the chain with more than one low-impedance loads at the same time, thus affecting the overall input matching and the proper operation of the TTD cells. To alleviate this problem, two separate chains of TTD cells are employed. The two chains are excited using the same signal generator . The first and second chains are responsible for generating the inputs of the correlator and , respectively, as shown in Fig. 16. For example, to detect the permittivity in the first sub-frequency range ( and ), and are selected from chains 1 and 2, respectively, and applied to the correlator to have an output voltage proportional to . For the second sub-frequency range ( and ), and are selected from chains 1 and 2, respectively, for a correlator output proportional to . Further signal switching is then performed to cover the entire 1–8-GHz frequency range. Single-pole dual-throw (SPDT) RF switches are used to select the signals and from chains 1 and 2 according to the sub-frequency range using the control signals . The signals selected from chains 1 and 2 are then applied to correlators. In this design, two correlators are used. Correlator 1 covers the frequency range up to 3.5 GHz ( and ) and correlator 2 covers the frequency range up to 8 GHz ( and ), as will be shown in Section IV. Fig. 16 shows an example of the switching setup used to detect the permittivity in the first sub-frequency range where the switches and are activated to connect and to correlator 1. The output of correlator 1 is then proportional to . Two 50- resistors ( and ) are inserted in series with each chain to make the overall impedance seen by the signal generator to be 50 for proper input matching. The use of these resistors helps in input matching at the cost of power loss for each chain of TTD cells. Table I shows different switching configurations for different sub-frequency ranges, the corresponding selected signals and the corresponding values of and detected phase shifts. The sub-frequency ranges are overlapping to ensure full coverage of the sensing frequencies in the 1–8-GHz range. For example, in sub-frequency range 3, switches and in TTD chains 1 and 2 are activated to enable correlation between and . The phase shift between and is equal to , which is the phase shift corresponding to ten cascaded TTD cells.

IV. CIRCUIT IMPLEMENTATION AND TEST SETUP The dielectric spectroscopy system is fabricated on Rogers Duroid substrates with a total area of 8 7.2 cm . The passive TTD cell is similar to the one shown in Fig. 6 and multiple TTD cells are arranged in cascade, as shown in Fig. 8. Correlation and switching in Fig. 16 are performed using commercial discrete

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Fig. 16. Block diagram of the dielectric spectroscopy system. The bold lines in red (in online version) represent the switching setup for permittivity detection in and ). the first sub-frequency range ( TABLE I DIFFERENT SWITCHING COMBINATIONS FOR THE SYSTEM IN FIG. 15 ALONG WITH CORRESPONDING SIGNALS, FREQUENCY RANGE, AND DETECTED PHASE SHIFT

Fig. 17. Photograph of the fabricated sensor.

components. SPDT switches are packaged RF microelectromechanical systems (MEMS) switches (2SMES-01),2 operating up to 10 GHz. A dc voltage of 34 V is used for actuation achieving a high isolation when open ( 30 dB) and a low insertion loss when closed ( 1 dB) up to 8 GHz. 2Omron

Inc., Schaumburg, IL. [Online]. Available: www.omron.com

THE

Correlators are implemented using discrete surface mount double-balanced passive mixers from Mini-Circuits.3 Two mixers are used to cover the entire frequency range from 1 to 8 GHz with a conversion loss 7 dB: 1) MCA1-42 used for detection in sub-frequency ranges 1–3 covering the 1–3.5-GHz frequency range and 2) MCA1-80LH used for detection in sub-frequency ranges 4–6 covering the 3.5–8-GHz frequency range. Fig. 17 shows the photograph of the fabricated sensor using two chains of TTD cells, four SPDT switches, two passive mixers with necessary components for biasing, and RF/dc input/output connections. The effect of capacitive and resistive loading of the switches in the OFF and ON states and the mixers should be considered regarding: 1) the input impedance matching and 2) the detection accuracy. For impedance matching, EM simulation of TTD cells is performed along with the reported -parameters of the switches in both ON and OFF states and the mixers. This simulation adds fine tuning to the dimensions of the TTD cell to achieve proper input/output return loss and a phase-frequency response for the sensor similar to the one shown in Fig. 10. For example, the capacitive loading of the switch mandates slight decrease in the sensing and fixed capacitors to compensate for this extra added capacitance. Moreover, for more accurate detection and measurements, sensor calibration needs to be 3Mini-Circuits Inc., Brooklyn, NY. [Online]. Available: www.minicircuits.com

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Fig. 18. (a) Photograph of the tube on top of the sensing elements. (b) Photograph of the micropipette used to insert liquids under test inside the tube.

performed as an initial step before permittivity detection to de-embed the effect of any nonidealities, loading, and mismatches, as shown in Section V-A. For chemical sensing, the liquids under test are contained in plastic cylindrical tubes fixed and glued on top of the sensing elements in both TTD chains in a way similar to the one reported in [29]. The effect of the plastic tubes was not considered in the EM simulations using Sonnet in Fig. 13. However, the similarity between the simulations and prototype measurements employing the plastic tubes in Fig. 13 proves minimal effect of these tubes on the permittivity detection. Moreover, the effect of the plastic tube on the capacitance of the sensing elements is constant regardless of the permittivity of material deposited on top of the sensor. Accordingly, sensor calibration procedure discussed in Section V-A can remove any effect from the plastic tube on the detected permittivity. Fig. 18(a) shows a photograph of a tube glued on top of TTD cells in one of the TTD chains. A Finnpipette single-channel micropipetter4 shown in Fig. 18(b) is used to insert liquids under test inside the tubes with 0.2- L resolution and to remove the liquids from the tubes after sensing. Commercial gas dusters5 are used to clean the TTD cells from any residues of deposited liquids. V. EXPERIMENTAL PROCEDURES AND RESULTS The frequency dependency of the permittivity of organic chemicals can be represented by the Cole–Cole model given by [11] (14) is the static permittivity at zero frequency, is where the permittivity at is the relaxation time, and is the distribution (relaxation time) parameter. These constants are specific for each organic chemical. Moreover, the intensity of EM fields around the sensing capacitor depends on the volume of MUT deposited on top of the sensing elements. Therefore, the sensing process is performed for organic chemicals while sweeping two independent parameters, which are: 1) the sensing frequency , which is tuned by changing the frequency of the input microwave signal, , in the range of 1–8 GHz and 2) the sample volume , which is tuned by inserting different volumes of liquids inside the tubes on top of the sensing elements 4[Online].

Available: http://www.thermoscientific.com

5[Online].

Available: www.dust-off.com

Fig. 19. Fitted versus characteristics at volumes ranging from 50 to 250 L at the sensing frequency of 1 GHz.

Fig. 20. Standard deviation of the correlator’s output voltage as a function of at a frequency of 1 GHz. the sample volume

using the micropipette. Sample volumes are tuned within the range of 50–250 L. Organic chemicals are subject to permittivity detection, including: 1) alcohols: ethanol (CH –CH –OH), Methanol (CH –OH), Isopropanol (CH –CH –CH–OH) and II-butyl-alcohol (CH –CH–OH–CH –CH ); 2) ketones: acetone (CH –CH –CO); 3) esters: ethyl-acetate (CH –COO–CH –CH ); and 4) alkyl benzenes: xylene (C H –CH –CH ). The objective is to detect the permittivity of each material at a given sensing frequency and sample volume . The sensing system is measured by applying a sinusoidal signal using Agilent E8267D microwave signal generator for the 1–8-GHz frequency range with a frequency step of 0.4 GHz. First, the sensor is characterized using calibration materials to find the sensor’s characteristic curves relating the output voltage from the correlator and the permittivity of the MUT at each sensing frequency and sample volume. Second, unknown organic chemicals under characterization are deposited and the measured output voltage from the correlator is used along with the sensor’s characteristic curves to find the permittivity of MUT . This procedure is explained in more detail as follows.

HELMY AND ENTESARI: 1–8-GHz MINIATURIZED SPECTROSCOPY SYSTEM FOR PERMITTIVITY DETECTION AND MIXTURE CHARACTERIZATION

Fig. 21. Contour plots showing the variations of the fitting parameters with sensing frequency , and (c) .

A. Sensor Characterization: Versus Curves Using Calibration Materials

Characteristic

Air, ethanol, and methanol are used as calibration materials. Permittivities of the calibration (reference) materials are assumed to be known from the Cole–Cole models [11]. Each calibration material is deposited on top of the sensing elements and the output voltage of the correlator is read out at each sensing frequency and sample volume . with respect to reported The measured values of permittivities for the calibration materials are used to have a full versus characteristics for each value of sample volume and sensing frequency using curve fitting. Since three calibration materials are used, curve fitting is limited to second-order (quadratic) polynomials. Increasing the number of materials used for calibration increases the order of the polynomial fitting function and improves the detection accuracy. Employing three calibration materials is proved to be enough for a good accuracy of permittivity detection, as will be shown later. The versus characteristic equation is represented as (15) and are the polynomial fitting parameters and are where functions of sensing frequency and the sample volume . Fig. 19 shows the fitted versus characteristics at volumes ranging from 50 to 250 L at the sensing frequency of 1 GHz as an example. These plots can be used to extract the values of , , and at 1 GHz for different values of using curve fitting. Fig. 20 shows the standard deviation of the correlator output voltage over 20 different trials at 1 GHz. The standard deviation decreases with increasing the sample L at which volume and reaches a value of 2% for the EM fields are well confined around the sensing elements. Plots similar to Fig. 19 and 20 are generated for frequencies in the range of 1 to 8 GHz with a frequency step of 0.4 GHz. The dependency of the standard deviation on the sample volume at all frequencies is similar the one at 1 GHz (Fig. 20). As the mean values of the fitting parameters ( , , and ) over the 20 different trials are dependent on both the sensing

and the sample volume

: (a)

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, (b)

frequency and sample volume, contour plots are used to illustrate this dependency, as shown in Fig. 21(a)–(c). The values of , , and in Fig. 21 are used for characterization of unknown organic chemicals in the next step of the sensing procedure. B. Dielectric Spectroscopy of Organic Chemicals Organic chemicals are subject to permittivity detection in the frequency range of 1–8 GHz, including acetone, ethyl acetate, isopropanol, II-butyl alcohol, and xylene. In order to detect the permittivity of an organic chemical at a given sensing frequency and sample volume , the sensing process is performed in three steps. 1) Characteristic Equation: Extract the values of the fitting parameters ( , , and ) corresponding to the sensing frequency and sample volume from the contour plots in Fig. 21. 2) Material Sensing: The frequency of the microwave signal generator is set to and a volume of of the MUT is deposited on top of the sensing elements. The voltage at the output of the correlator is then detected. 3) Permittivity Computation: Using the extracted values of , , and ; and the detected voltage at the output of the correlator , the value of permittivity, , is found as follows: (16) where (17) Similar procedure is repeated for other chemicals at all values to perform full dielectric spectroscopy of MUT for of and 1–8-GHz frequency range. As an example, ethyl acetate is characterized at GHz and L. The above sensing procedure is applied as follows. • The extracted values of , , and are 70 10 , 6.8 10 , and 0.87; respectively. Accordingly, the characteristic equation is given by GHz L .

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Fig. 23. Measured points for isopropanol ( L) with the extrapolated curve to estimate the permittivity of isopropanol at frequencies below 1 GHz.

elements. The value of does not change for volumes larger than 200 L at which the measurement results for the organic chemicals are very close to the theoretical values based on Cole–Cole models [11]. This is because EM fields are well confined around the sensing capacitors for these volumes and the EM field intensity becomes independent of . The absolute value of the relative error between the measured permittivities at L and the theoretical values is less than 2%. Error bars in Fig. 22 show the variance of measured points (20 different trials) around the mean values for L. VI. APPLICATIONS

TO

AND

DIELECTRIC CHARACTERIZATION SPECTROSCOPY

A. Estimation of Permittivities at Low Frequencies As mentioned before, one of the advantages of broadband dielectric spectroscopy is the possibility to detect the low-frequency permittivity of samples using extrapolation. The detected permittivities of MUTs in Fig. 22 in the frequency range of 1–8 GHz are used to estimate the values of of these materials at frequencies below 1 GHz, especially at zero frequency. This can be done by fitting the measured points in Fig. 22 to a polynomial function given by (18) Fig. 22. Measured permittivities versus frequency for different volumes for: (a) isopropanol and ethyl acetate, (b) xylene and II-butyl alcohol, and (c) acetone. The measured permittivity is compared with theoretical values from (14).

• 250 L of ethyl acetate is deposited and the frequency of the signal generator is set to 1 GHz. The measured correlator’s output voltage (1 GHz, 250 L) is found to be 0.848 V. • Substituting the values of (1 GHz, 250 L), , , and in (16) and (17) results in a permittivity (1 GHz, 250 L) of 6.7. Fig. 22(a)–(c) shows the average measured values of of different organic chemicals versus the sensing frequency for different values of over 20 different trials. Fig. 22 shows that the accuracy of detection of increases with increasing the volume of liquid deposited on top of the sensing

where are the coefficients of the polynomial function, is the polynomial order, and is the frequency in gigahertz. The higher the order of the polynomial is, the higher the fitting accuracy is. The values of at frequencies below 1 GHz can then be found by substituting in (18). As an example, the measured points of isopropanol for L are fitted to a fifth-order polynomial function . This polynomial function is plotted for all frequencies between 0–8 GHz along with the measured points in the 1–8-GHz range, as shown in Fig. 23. The permittivity of isopropanol at zero frequency is estimated to be 20.1 compared to a theoretical value of 20.24 [11]. Similar procedure with fifth-order polynomial fitting is repeated for other MUTs and the zero-frequency permittivity is estimated and compared to the theoretical value, as shown in Table II, with an error less than 2%.

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TABLE II ESTIMATED AND THEORETICAL STATIC PERMITTIVITIES OF MUTs

B. Mixture Dielectric Characterization Mixture characterization can be performed using permittivity [17], thermal conductivity [30], [31], mass density, and viscosity [32], [33] of mixtures as parameters for composition detection. Most of the reported miniaturized mixture detectors using thermal conductivity, mass density, and viscosity are based on micromachined structures, such as bridges, cantilevers, clamped beams, and suspended MEMS resonators [30]–[33]. The advantage of the proposed system for mixture detection using permittivity sensing is the planar property of the sensing element, which results in simpler fabrication compared to other techniques. In this section, the dielectric spectroscopy system is employed to characterize binary mixtures. Mixing two different materials, host and guest, with complex permittivities of and and mixing ratios of and ; respectively, results in an effective complex permittivity given by [34], [35]

(19) and correwhere is a dimensionless parameter and sponding to different mixtures theoretical equations: Maxwell Garnett, Polder-van Santen, and coherent potential models; respectively [34], [35]. The sensing procedure in Section V is employed to characterize ethanol (host)–methanol (guest) mixtures. Characteristic equations developed in Section V for different sensing frequencies and sample volumes are employed in mixture characterization. For example, the ethanol–methanol binary mixture is characterized at GHz and L with fractional volumes of and , respectively. The sensing process described in Section V is performed as follows. 1) At GHz and L, the values of , , and are 58 10 7.43 10 and 0.773, respectively. 2) Using the micropipette, 50 L of ethanol and 200 L of methanol are mixed together and deposited on top of the sensing cells. The frequency of the signal generator is set to 4.5 GHz and the output voltage of the correlator is found to be 0.77 V. 3) Using the values of , , and and (16) and (17), the value of the permittivity is found to be 6.26. A similar procedure is applied for all values of between 0 and 1. Fig. 24 shows the average values of the detected dielectric constant of the ethanol–methanol mixture [ ( GHz, L)] versus over ten different trails compared with one of the theoretical mixture models [ in (19)]. Zoomed portion of versus within the ranges of and

Fig. 24. Measured and theoretical permittivities versus the mixing ratio for L and GHz with the ethanol–methanol binary mixture at and . zoomed views at

are also shown. Fig. 24 shows detected permittivities are very close to theoretical values with a relative error less than 2% with a fractional volume accuracy of 1%. Error bars in Fig. 24 show the variance of the ten measured points around the mean values for and . VII. CONCLUSION A miniaturized platform for broadband dielectric spectroscopy system has been developed for permittivity detection of organic chemicals for the frequency range of 1–8 GHz. The design of cascaded TTD cells to detect the frequency dependent permittivity has been presented in detail considering nonideal effects such as the EM coupling between adjacent cells. The spectroscopy system, including TTD cells, correlators, and SPDT switches, has been calibrated using reference materials. Using a unique detection procedure, the system is demonstrated to detect the permittivity of organic chemicals in the frequency range of 1–8 GHz, and estimate the zero-frequency permittivity using extrapolation with an accuracy of 2%. The system is also used to characterize the mixing ratios in binary mixtures to around 1% fractional volume. REFERENCES [1] G. Smith, A. Duffy, J. Shen, and C. Olliff, “Dielectric relaxation spectroscopy and some applications in the pharmaceutical applications,” J. Pharmaceut. Appl., vol. 84, no. 9, pp. 1029–1044, Sep. 1995. [2] A. Lonappan, V. Thomas, and G. Binda, “Non-destructive measurement of human blood at microwave frequencies,” J. Electromagn., Waves, Appl,, vol. 21, no. 8, pp. 1131–1139, 2007. [3] H. F. Cook, “Dielectric behaviour of human blood at microwave frequencies,” Nature, vol. 168, pp. 247–248, 1951. [4] A. Lonappan, G. Binda, and V. Thomas, “Analysis of human semen using microwaves,” Progr. Electromagn. Res., pp. 277–284, 2006. [5] A. Lonappan, V. Thomas, and G. Binda, “Analysis of human cerebra spinal fluid at the ISM band of frequencies,” J. Electromagn., Waves, Appl., vol. 20, no. 6, pp. 773–779, 2006. [6] K. Kim, L. Kim, S. Lee, and S. Noh, “Measurement of grain moisture content using microwave attenuation at 10.5 GHz and moisture density,” IEEE Trans. Instrum. Meas., vol. 51, no. 1, pp. 72–77, Feb. 2002. [7] H. Al-Mattarneh, D. Ghodgoankar, and W. Majid, “Microwave nondestructive testing for classification of Malaysian timber using freespace techniques,” in Proc. 6th Int. Signal and Its Appl., Kuala Lumpur, Malaysia, 2001, vol. 2, pp. 450–453.

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[8] P. Banerjee, G. Ghosh, and S. Biswas, “A system to measure dielectric constant and loss of liquids at microwave frequencies,” in IEEE Appl. Electromagn. Conf., Dec. 2009, pp. 71–72. [9] Y. Hayashi, L. Livshits, A. Caduff, and Y. Feldman, “Dielectric spectroscopy study of specific glucose influence on human erythrocyte membranes,” J. Appl. Phys., vol. 36, pp. 369–374, 2003. [10] A. M. Campbell, “Development of computer modelling techniques for microwave thermography,” Ph.D. dissertation, Dept. Phys. Astron., Univ. Glasgow, Glasgow, U.K., 1989. [11] K. S. Cole and R. H. Cole, “Dispersion and absorption in dielectrics I. Alternating current characteristics,” J. Chem. Phys., vol. 9, no. 4, pp. 341–351, Apr. 1941. [12] C. Wakai, A. Oleinikova, M. Ott, and H. Weingartner, “How polar are ionic liquids? Determination of the static dielectric constant of an imidazolium-based ionic liquid by microwave dielectric spectroscopy,” J. Phys. Chem. Lett., vol. 109, no. 36, pp. 17028–17030, 2005. [13] G. Cheng, C. Yuan, X. Ma, and L. Liu, “Multifrequency measurements of dielectric properties using a transmission-type overmoded cylindrical cavity,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 5, pp. 1408–1418, May 2011. [14] U. C. Hasar, “A new microwave method for electrical characterization of low-loss materials,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 12, pp. 801–803, Dec. 2009. [15] K. Grenier, D. Dubuc, P.-E. Poleni, M. Kumemura, H. Toshiyoshi, T. Fujii, and H. Fujita, “Integrated broadband microwave and microfluidic sensor dedicated to bioengineering,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 12, pp. 3246–3253, Dec. 2009. [16] B. L. McLaughlin and P. A. Robertson, “Submillimeter coaxial probes for dielectric spectroscopy of liquids and biological materials,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 12, pp. 3000–3010, Dec. 2009. [17] K. Saeed, A. C. Guyette, I. C. Hunter, and R. D. Pollard, “Microstrip resonator technique for measuring dielectric permittivity of liquid solvents and for solution sensing,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007, pp. 1185–1188. [18] K. Saeed, R. D. Pollard, and I. C. Hunter, “Substrate integrated waveguide cavity resonators for complex permittivity characterization of materials,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 10, pp. 2340–2347, Oct. 2008. [19] P. A. Bernard and J. M. Gautray, “Measurement of dielectric constant using a microstrip ring resonator,” IEEE Trans. Microw. Theory Techn., vol. 39, no. 3, pp. 592–595, Mar. 1991. [20] Y. Feldman, I. Ermolina, and Y. Hayashi, “Time domain dielectric spectroscopy study of biological systems,” IEEE Trans. Dielectr. Electr. Insulation, vol. 10, no. 5, pp. 728–753, Oct. 2003. [21] J. Zhuang, K. H. Schoenbach, and J. F. Kolb, “Time domain dielectric spectroscopy of biological cells after pulsed electric field exposure,” in 2011 Electr. Insulation and Dielectr. Phenomena Conf. Annu. Rep., Oct. 16–19, 2011, pp. 44–47. [22] A. Cataldo, L. Tarricone, F. Attivissimo, and A. Trotta, “A TDR method for real-time monitoring of liquids,” IEEE Trans. Instrum. Meas., vol. 56, no. 5, pp. 1616–1625, Oct. 2007. [23] A. A. Helmy and K. Entesari, “A 1-to-8 GHz miniaturized dielectric spectroscopy system for chemical sensing,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 17–22, 2012, pp. 1–3. [24] T. Hancock and G. Rebeiz, “A 12 GHz SiGe phase shifter with integrated LNA,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 3, pp. 977–983, Mar. 2005. [25] C. Veyres and V. Fouad-Hanna, “Extension of the application of conformal mapping techniques to coplanar lines with finite dimensions,” Int. J. Electron., vol. 48, no. 1, pp. 47–56, Jan. 1980. [26] G. Ghione and M. Goano, “Revisiting the partial-capacitance approach to the analysis of coplanar transmission lines on multilayered substrates,” IEEE Trans. Microw. Theory Techn., vol. 51, no. 9, pp. 2007–2014, Sep. 2003. [27] A. Maric, G. Radosavljevic, L. Zivanov, and G. Stojanovic, “A simple approach for modelling and simulation monolithic inductors,” in Int. Semiconduct. Conf., Oct. 12–14, 2009, vol. 2, pp. 459–462.

[28] N. Suwan, “Investigation of RF direct detection architecture circuits for metamaterial sensor applications,” M.S. thesis, Dept. Elect. Comput. Eng., Univ. of Waterloo, Waterloo, ON, Canada, 2011. [29] V. Sekar, W. Torke, S. Palermo, and K. Entesari, “A self-sustained microwave system for dielectric constant measurement of lossy organic liquids,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 5, pp. 1444–1455, May 2012. [30] R. Beigelbeck, H. Nachtnebel, F. Kohl, and B. Jakoby, “A novel measurement method for the thermal properties of liquids by utilizing a bridge-based micromachined sensor,” J. Meas. Sci. Technol., vol. 22, no. 10, pp. 1–9, 2011. [31] J. Kuntner, A. Jachimowicz, F. Kohl, and B. Jakoby, “Determining Thermal Properties of Liquids: Membrane-based versus bridge-based micromachined sensors,” in IEEE Sensors Conf., Oct. 22–25, 2006, pp. 1411–1414. [32] S. Cerimovic, R. Beigelbeck, H. Antlinger, J. Schalko, B. Jakoby, and F. Keplinger, “Sensing viscosity and density of glycerol water mixtures utilizing a suspended plate MEMS resonator,” J. Microsyst. Technol., vol. 18, no. 7–8, pp. 1045–1056, 2012. [33] C. Riesch, A. Jachimowicz, F. Keplinger, E. K. Reichel, and B. Jakoby, “A micromachined doubly-clamped beam rheometer for the measurement of viscosity and concentration of silicon-dioxide-in-water suspensions,” in IEEE Sensors Conf., Oct. 26–29, 2008, pp. 391–394. [34] A. Sihvola, “Mixing rules with complex dielectric coefficients,” J. Subsurface Sensing Technol. Appl., vol. 1, no. 4, pp. 393–415, 2000. [35] A. Sihvola, “Self-consistency aspects of dielectric mixing theories,” IEEE Trans. Geosci. Remote Sens., vol. 27, no. 4, pp. 403–415, Jul. 1989.

Ahmed A. Helmy (S’09) was born in Cairo, Egypt, in 1983. He received the B.Sc. degree (with honors) and M.Sc. degree in electronics and communications engineering from Cairo University, Giza, Egypt, in 2005 and 2008, respectively, and is currently working toward the Ph.D. degree in electrical and computer engineering at Texas A&M University, College Station. From 2005 to 2008, he was a Research Assistant with the Yousef Jameel Science and Technology Research Center, The American University, Cairo, Egypt. From 2005 to 2008, he was a Teaching Assistant with the Electronics and Communications Engineering Department, Cairo University. In Summer 2011, he was an RF Design Intern with Samsung Telecommunications America, Dallas, TX, where he was involved with millimeter-wave wireless transceivers design. His research interests include RF integrated circuit (RFIC) design, CMOS sensors, and MEMS.

Kamran Entesari (S’03–M’06) received the B.S. degree in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 1995, the M.S. degree in electrical engineering from Tehran Polytechnic University, Tehran, Iran, in 1999, and the Ph.D. degree from The University of Michigan at Ann Arbor, in 2005. In 2006, he joined the Department of Electrical and Computer Engineering, Texas A&M University, College Station, where he is currently an Associate Professor. His research interests include the design of RF/microwave/millimeter-wave integrated circuits and systems, RF MEMS, and microwave chemical/biochemical sensing. Dr. Entesari was the recipient of the 2011 National Science Foundation (NSF) CAREER Award for his work on fully integrated versatile broadband microwave dielectric spectroscopy systems. He was the co-recipient of the 2009 Semiconductor Research Corporation (SRC) Design Contest Second Project Award for his work on dual-band millimeter-wave receivers on silicon.

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Accurate Nanoliter Liquid Characterization Up to 40 GHz for Biomedical Applications: Toward Noninvasive Living Cells Monitoring Tong Chen, David Dubuc, Member, IEEE, Mary Poupot, Jean-Jacques Fournié, and Katia Grenier, Member, IEEE

Abstract—This paper demonstrates an accurate liquid sensing technique, from 40 MHz to 40 GHz, which is suitable for the detection and quantification of very small contents of molecules, proteins, and for the noninvasive and contactless microwave investigation of living cells in their culture medium. The sensor is based on an interdigitated capacitor (IDC) with a microfluidic channel to confine the nanoliter-range liquid and is integrated with microtechnologies to be fully compatible with a massive parallelization at low cost. Both alcohol and biological aqueous solutions are precisely characterized, identified, and quantified in terms of capacitance and conductance’s contrasts with respect to pure de-ionized water. Mixtures from 20% down to 1% of ethanol in water exhibit large capacitance’s values of 110 and 7 fF at 11 GHz, respectively. Based on the high accuracy of such characterizations, the detection of very small traces of ethanol (down to 100 ppm) can be envisioned. As far as biomedical applications are targeted, we also demonstrate the potential of fetal bovine serum detection in aqueous solution down to 5% v/v. Finally, the sensor is evaluated with living B lymphoma cells suspension in their traditional biological medium. The in-liquid microwave measurement of less than 20 living cells is successfully performed and corresponds to a capacitance contrast of 5 fF at 3 GHz relative to the reference bio-medium. For low cells concentration, the sensor response is proportional to the number of cells on the IDC, which permits to envision cells quantification and proliferation monitoring with this microwave sensing technique. Index Terms—Biology, biomedical transducers, human cells, interdigitated capacitor (IDC), microwave spectroscopy.

I. INTRODUCTION

T

HE integration of analytic sensing techniques of liquids is of prime importance for applications in chemistry, biochemistry, biology and medicine [1]. During the past years, intensive research are indeed on going to miniaturize biosensors as well as to reduce assays time without compromising selectivity and sensitivity to molecules or cells under analysis [2]. Among all the miniaturizable physical transductions methods (optical, mechanical, electrochemical), the electrical one and

Manuscript received July 10, 2012; revised September 21, 2012; accepted September 25, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported by under a French RITC Foundation Grant. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. T. Chen, D. Dubuc, and K. Genier are with the National Scientific Research Center, Laboratory of Analysis and Architecture of Systems (LAAS), 31400 Toulouse, France (e-mail: [email protected]). M. Poupot and J.-J. Fournié are with the Cancer Research Center of Toulouse, Toulouse, 31000 France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222660

more specifically the dielectric spectroscopy is one of the most promising techniques, since it does not require any bio-functionalization or labeling protocols. This ability avoids any targetlabel coupling reactions or main assay alteration, as well as it assures inexpensive and time-efficient operation [3]. Moreover, dielectric spectroscopy analysis techniques operating in the gigahertz frequencies reveal a rich set of bio-information [4] based on the molecular content of the medium under investigation: dielectric polarization and relaxation phenomenon and interactions between molecules notably. In the case of living cells analysis, the operation in the microwave range translates into a full electromagnetic (EM) waves penetration inside the intracellular content [5], which makes the probing able to discriminate physiological state of cell (living/ dead, normal/tumorous, ). This paper presents a biosensor resulting from the combination of both the microwave-based liquid sensing technique [5]–[7] with microfluidics capabilities [8] and able to detect and quantify very small contents of molecules, proteins, and living cells in their culture medium. The device operates in the nanoliter range, which assures very low consumed volume of liquids required for high throughput analysis. The developed technique provides an accurate identification and quantification of very low content of molecules (down to 100 ppm in the case of ethanol) in aqueous solution. Moreover, a population of only 20 living cells has been accurately characterized in their liquid microenvironment. In addition to the label-free ability of the technique, its capability to operate with biological medium (i.e., featuring a high ionic content) opens new and innovative way for noninvasive cell analysis and real-time monitoring. This paper is organized as follows. Section II is dedicated to sensor description and simulations. Section III deals with the experimental validation of the approach, whereas Section IV discusses the experimental results obtained with references binary liquid mixtures based on aqueous solutions, which feature various solutes’ concentrations. Finally, Section V deals with the evaluation of the sensor in term of cells concentration with living human lymphoma cells in suspension. II. SENSOR DESCRIPTION AND SIMULATIONS The considered nanoliter liquid sensor is based on an interdigitated capacitor (IDC) embedded into a coplanar waveguide, as presented in Fig. 1. The dielectric sensing area is, in this design, a square of 150 150 m and can be easily down-scaled. The liquid confinement is assured with a microfluidic channel composed of polydimethylsiloxane (PDMS), which features a height

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Fig. 1. Schematic of the IDC with a narrowed microfluidic channel placed on top.

Fig. 3. Calculated distribution of the electric-field magnitude of the IDC loaded with liquid for two configurations. (a) Top view. (b) Cross section.

Fig. 2. Photograph of the fabricated microfluidic IDC with a PDMS channel.

of 40 m. This elastomer has the main advantages of being biocompatible, cheap, and simply molded. Its transparency allows an easy observation of the biological material placed in the channel, and notably living cells. However, its high losses in the microwave and millimeter-wave ranges impose to minimize the sidewalls’ width of the channel, which are located in the direct vicinity of the EM fields. The walls of the fluidic channel are thus limited to a width of 200 m on top of the coplanar device. The main liquid passage is 980- m wide to facilitate the injection of the fluid, whereas the narrow one in the sensing area is about 150 m, as presented in Fig. 2. The volume of the analyzed liquid is consequently about 0.9 nL. The IDC presents strips and slots of 10- m width. The microwave electrodes are made of 300-nm-thick titanium and gold layers on top of a quartz wafer to minimize additional dielectric losses due to the substrate. The fabrication of the biosensor is based on standard microtechnological processes. It may be divided in two main parts, which are: 1) the elaboration of the IDC on a quartz wafer and 2) the polymer microfluidic channel elaboration and assembling. All the corresponding details may be found in [9]. To evaluate the electric-field distribution in the sensing area of the IDC, a 3-D finite-element method (3-D FEM) analysis is performed using Ansoft’s High Frequency Structure Simulator (HFSS). Fig. 3(a) and (b) presents a top view and a cross section of the calculated field, respectively.

As expected for such a component, the electric field is strongly concentrated in the IDC region and in the vicinity of the coplanar slots. The PDMS channel is consequently limited to the centered area of the IDC to enhance the interaction between the EM wave and the liquid sample in this preferred area. As far as the cross section is concerned, the field is more intense the first 15 m above the capacitor [represented in red (in online version) in Fig. 3(b)]. The field, however, extends to the top of the microchannel (in green in online version), which means that the entire volume of liquid is fully analyzed with the IDC device in the sensing area. Based on these preliminary design considerations, a protocol to extract the complex admittance parameters of the IDC is defined. III. EXTRACTION OF THE COMPLEX ADMITTANCE PARAMETERS AND VALIDATION WITH DE-IONIZED WATER (DI WATER) The electrical characterization of the IDC is performed on wafer from 40 MHz to 40 GHz. The liquid injection inside the microfluidic channel is precisely controlled with a syringe pump from Harvard Apparatus, Holliston, MA. Measurements are then treated to extract the complex admittance parameters of the IDC loaded with different types of liquids. The protocol of extraction is based on the IDC’s electrical model, which is given in Fig. 4. It includes two access transmission lines (TLs) at the input and output, two capacitors with one related to the

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IV. EVALUATION OF THE SENSOR WITH REFERENCED BINARY LIQUID MIXTURES The nanoliter liquid IDC is evaluated to accurately characterize referenced binary liquid mixtures. Two types of solutions are investigated. The first one is related to alcohol-based aqueous solutions, whereas the second one corresponds to fetal bovine serum (FBS) in water in order to assess biological liquids in agreement with a realistic environment of cells in suspension. To better define the sensitivity of the sensing technique for aqueous-based solutions, we extract the IDC complex admittance values’ contrasts of the mixtures relative to pured DI water, which is the main constituent of the solutions. They are defined with (3) and (4), respectively, as follows:

Fig. 4. Electrical model of the IDC.

(3) (4) These contrasts of capacitance and conductance better refer to a variation of a chemical proportion in the referenced DI-water liquid. A. With Alcohol-Based Aqueous Solutions

Fig. 5. Capacitance and conductance of the fluidic part of the IDC.

quartz substrate and the other one associated to the fluid, and a conductance related to the losses induced by the fluid. First, a de-embedding procedure is applied to subtract the effect of the coplanar access lines. Both capacitance and conductance related to the fluid are then calculated. Fig. 5 presents the corresponding extracted IDC values versus frequency (solid line), when the structure is loaded with DI water. In order to validate the extraction procedure, an EM simulation of the structure is also performed. The relative complex permittivity of water is taken into account with the Debye relaxation model, which is given by (1) and (2) as follows:

(1)

(2)

, , and correspond to the real parts of the where relative permittivity at very low and very high frequencies and to the Debye relaxation frequency, respectively. These parameters are optimized with the technique previously developed [10]. The predicted capacitor, extracted from the simulation, is presented in Fig. 5 via diamond marks. A good agreement between measurements and simulations is reached, which validates the correct operation of the developed nanoliter liquid sensor.

Four concentrations of ethanol in DI water are measured: 20%, 10%, 5%, and 1%. The corresponding capacitive and conductive contrasts versus frequency are presented in Fig. 6(a) and (b), respectively. All concentrations lead to significant contrasts on both - and -parameters, even for the lowest tested concentration of 1% of ethanol and with nanoliter volumes of liquids. These results are explained by the strong value difference that exists between the respective dielectric constants of ethanol and DI water. Moreover, the use of contrasts spectra also permits to establish the most appropriate frequency range for which the sensitivity for such solvent-based binary mixtures is maximal on both and readouts. In the case of ethanol in DI water, the range related to the largest capacitance contrast is located from 10 to 13 GHz for the investigated concentrations. A maximal capacitance contrast of 112 fF is obtained at 11 GHz for a 20% concentration of solvent in water. Fig. 7 indicates the obtained capacitive contrast versus the composition of the mixture. In the considered concentration range, the capacitance contrast is proportional to the ethanol concentration in water. Due to the large capacitance variation of 34 fF at 11 GHz (for 5% of ethanol volume content) and by considering the sensitivity level close to 0.1 fF, the presented IDC structure lets one envision distinguishing very small solute contents in aqueous solution, as low as a few 100 ppm. Such a rationale may also be performed with the second accessible readout of the microwave sensing technique, the conductance. As shown in Fig. 6(b), the maximal contrast of this parameter is reached at 40 GHz, the highest measured frequency of this study, for all investigated ethanol concentrations. A 16-mS conductance contrast is obtained for the 20% concentration of ethanol. To briefly conclude this section, the microwave sensing technique permits to analyze nanoliter volumes of liquids and gives access through two readouts ( and ) to the accurate composition of binary solvent-based mixtures in aqueous solution.

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Fig. 8. Contrast spectra of the: (a) capacitance and (b) conductance of biological-based aqueous solutions. Fig. 6. Contrast spectra of the: (a) capacitance and (b) conductance of alcoholbased aqueous solutions.

This measurement method is also applied to biological-based aqueous solutions. The corresponding results are presented in Section IV-B. B. With Biological-Based Aqueous Solutions

Fig. 7. Impact of the ethanol concentration in aqueous solution on the capacitance contrast, at 11 GHz.

Compared to planar TL-based sensors [10]–[15], our proposed technique efficiently gives access to liquid discrimination with a high level of accuracy, while being highly down-scalable to the nanoliter range and even further.

The chosen investigated biochemical corresponds to FBS, which is an important constituent of culture cell media. It provides important required nutrients to living cells for their survival and proliferation. Concentrations traditionally used by the biologists are in the range of 5%–10% in water. The extraction procedure of the complex admittance parameters, which was previously presented in Section IV-A, is applied and the results are presented in Fig. 8(a) and (b) for both capacitance and conductance contrasts, respectively. Similar to the solvent-based aqueous solutions, the contrasts on both and for the two concentrations of FBS are noticeable. The maximal constrasts for and are also obtained in the lower frequency part of the spectrum or in the highest part correspondingly. Their value ranges are, however, smaller than for ethanol. Whereas 10% of concentration of ethanol in water induces a maximal of 70 fF, the equivalent one for FBS (also for a concentration of 10% in water) is close to 9 fF. This

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Fig. 10. Cells distributions on the IDC for low, medium, and high concentrations of cells.

Fig. 9. Biological protocol to assure living cells incorporation in the IDC.

remark is also valid for the conductance contrast at 40 GHz. FBS composition is indeed strongly constituted of water with numerous ions, proteins, molecules, and other bio-constituents. The respective dielectric constant of DI water and FBS are consequently much closer than for ethanol. This result is all the more remarkable taking the ionic content into account. It reinforces the interest of using microwave sensors for biological analysis instead of lower frequency-based sensors, which are screened with conductive solutions. Based on a similar sensitivity approach as for ethanol, the detection of 0.1% in volume of FBS in an aqueous solution may be expected. As previously demonstrated for ethanol-based aqueous solutions, both and contrasts are proportional to the solutes concentration. Moreover, compared to the ethanol-based mixtures, the maximal contrasts on the capacitance are obtained at 3 GHz instead of 11 GHz (for ethanol-water mixtures). This is due to the different intrinsic relaxation frequency of each liquid. The spectra constitute consequently specific signatures of the analyzed liquids, which allow their identification. This part consequently demonstrates the ability with an IDC structure to probe biological material in liquid, in the nanoliter range with a sufficient accuracy. It opens the door to cells investigation in a confined microenvironment with appropriate conditions for cells living and even proliferation. With this purpose, we have investigated the impact of concentration of living cells in suspension in the IDC device. V. EVALUATION OF THE SENSOR IN TERM OF CELL CONCENTRATION WITH LIVING LYMPHOMA CELLS IN SUSPENSION Living B lymphoma cells suspensions are used in this study. They constitute a reference model for blood cancer investigations. To ensure the correct living pathological state of the cells during the experiments and reproducible investigations, we use the following biological protocol, which is described in Fig. 9. After the cells culture in a traditional incubator, the cells are collected and placed into an Eppendorf tube. They are then centrifuged to allow the elimination of the supernatant (consumed biological medium), which is replaced by a new and well-controlled culture medium. This one is composed of

Fig. 11. Contrast spectra of the: (a) capacitance and (b) conductance for different concentration of living RL lymphoma cells in their biological culture medium.

Roswell Park Memorial Institute (RPMI) medium with 10% of FBS. The quantity of added medium permits to control the concentration of cells. The living cells are then injected into the device for immediate measurements. Measurements are performed for three cell concentrations. The cells distributions in the sensing area of the IDC are given in Fig. 10. An optical observation permits to evaluate the number of cells for each condition. Consequently, values of about 20, 70, and 150 cells are obtained for low, medium, and high concentrations, respectively. Both capacitance and conductance contrasts are presented in Fig. 11. The reference liquid used for the calculation corre-

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REFERENCES

Fig. 12. Impact of the number of cells on the capacitance contrast at 3 GHz.

sponds this time to the biological medium, which is the host liquid of the cells. Similar to the previous study on binary mixtures, the cells concentrations in their biological medium can be discriminated with the IDC through the two readouts: the capacitance and conductance contrasts. The results are significant and well above the estimated sensitivity level of the sensor, even for the lowest concentration of cells. The frequency, which corresponds to the maximal contrast on the capacitance, is close to the one obtained with the FBS-based aqueous solution. Finally, the capacitance contrast is proportional to the number of cells in the sensing area. This is illustrated in Fig. 12, which presents the number of analyzed cells versus the extracted capacitance contrast at 3 GHz. The linear regression (dashed line in Fig. 12) of experimental data corresponds to a capacitive contrast per cell of 0.2 fF. Considering a sensitivity level of 0.1 fF, the detection of a single cell with the microwave sensing technique can be envisioned. These results suggest a possible cell counting and then cells proliferation monitoring from one single to hundreds of living cells. VI. CONCLUSION This paper has presented a miniature biosensor based on the interaction of a nanoliter-range aqueous solution with the EM waves at gigahertz frequencies. Besides the accurate detection of traces of alcohol (ethanol) and biological-based FBS in aqueous solutions, the detection and quantification of living lymphoma cells in their traditional culture medium are demonstrated. One of the major ability of such a technique resides in the in-culture medium analysis of cells, which assures a noninvasive operation on living cells. Combined with the markerless characteristic, this permits to analyze long-term bio-reactions without cells alteration by the sensor. It also allows reusing the cells after analysis for further investigations. The other major envisioned capability of the developed biosensor corresponds to the single cell detection and identification. This challenge combined with the already mentioned characteristics of the technique makes the proposed sensor highly attractive in regard to other competitors for laboratory-on-a-chip applications.

[1] R. Baw and J. Finkelsetein, “Lab on chip,” Nature, vol. 442, no. 7101, pp. 367–418, Jul. 2006. [2] R. Bashir, “BioMEMS: State-of-the-art in detection, opportunities and prospects,” Adv. Drug Del. Rev., vol. 56, pp. 1565–1586, 2004. [3] J. S. Daniels and N. Pourmand, “Label-free impedance biosensors: Opportunities and challenges,” Electroanalysis, vol. 19, no. 12, pp. 1239–1257, 2007. [4] S. Gabriel, R. W. Lau, and C. Gabriel, “The dielectric properties of biological tissues,” Phys. Med. Biol., vol. 41, no. 11, pp. 2231–2293, 1996. [5] H. P. Schwan, “Electrical properties of blood and its constituents: Alternating current spectroscopy,” Blut, vol. 46, pp. 185–197, 1983. [6] F. Kremer, “Dielectric spectroscopy—Yesterday, today and tomorrow,” J. Non-Cryst. Solids, vol. 305, no. 1–3, pp. 1–9, Jul. 2002. [7] F. Duhamel, I. Huynen, and A. Vander Vorst, “Measurement of complex permittivity of biological and organic liquids up to 110 GHz,” in IEEE MTT-S Int. Microw. Symp. Dig., 1997, vol. 1, pp. 107–110. [8] G. M. Whitesides, “The origins and the future of microfluidics,” Nature, vol. 442, pp. 368–373, Jul. 2006. [9] T. Chen, D. Dubuc, and K. Grenier, “Accurate nanoliter liquid complex admittance characterization up to 40 GHz for biomedical applications,” in IEEE MTT-S Int. Microw. Symp. Dig., Montréal, QC, Canada, Jun. 2012, pp. 1–3. [10] K. Grenier and D. Dubuc et al., “Integrated broadband microwave and microfluidic sensor dedicated to bioengineering,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 12, pp. 3246–3253, Dec. 2009. [11] G. R. Facer et al., “Dielectric spectroscopy for bio-analysis: From 40 Hz to 26,5 GHz in microfabricated waveguide,” Appl. Phys. Lett., vol. 78, no. 7, pp. 996–998, Feb. 2001. [12] J. C. Booth et al., “Quantitative permittivity measurements of nanoliter liquid in microfluidic channels to 40 GHz,” IEEE Trans. Instrum. Meas., vol. 59, no. 12, pp. 3279–3288, Dec. 2010. [13] S. S. Stuchly and C. E. Bassey, “Microwave coplanar sensors for dielectric measurements,” Meas. Sci. Technol., no. 9, pp. 1324–1329, 1998. [14] A. Raj, W. S. Holmes, and S. R. Judah, “Wide bandwidth measurement of complex permittivity of liquids using coplanar lines,” IEEE Trans. Instrum. Meas., vol. 50, no. 4, pp. 905–909, Apr. 2001. [15] S. Seo, T. Stintzing, I. Block, D. Pavlidis, M. Rieke, and P. G. Layer, “High frequency wideband permittivity measurements of biological substances using coplanar waveguides and application to cell suspensions,” in IEEE MTT-S Int. Microw. Symp. Dig., 2008, pp. 915–918.

Tong Chen received the M.S. degree in electrical engineering from the University of Toulouse, Toulouse, France, in 2009, and is currently working toward the Ph.D. degree at the University of Toulouse. He is currently with the Laboratory of Analysis and Architecture of System [part of the National Scientific Research Center (LAAS-CNRS)], Toulouse, France. His research interests involve the development of miniature microwave-based biosensors for dielectric spectroscopy.

David Dubuc (S’99–M’03) received the Agregation degree from the Ecole Normale Supérieure de Cachan, Paris, France, in 1996, and the M.S. and Ph.D. degrees in electrical engineering from the University of Toulouse, Toulouse, France, in 1997 and 2001, respectively. Since 2002, he has been an Associate Professor with the University of Toulouse, and a Researcher with the Laboratory of Analysis and Architecture of System, National Scientific Research Center (LAAS-CNRS), Toulouse, France. From 2007 to 2009, he was a Visiting Senior Researcher with the Laboratory of Integrated Micromechatronic Systems (LIMMS-CNRS)/Institute of Industrial Science (IIS), University of Tokyo, Tokyo, Japan. His research interests include the development of microwave circuits integrated due to microtechnologies and their application to wireless telecommunication and biology.

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Mary Poupot received the M.R. and Ph.D. degrees in biochemistry from the University of Paul Sabatier, Toulouse, France, in 1993 and 1997, respectively. From 2001 to 2007, she was a Postdoctoral Fellow with the Center of Physiopathology of Toulouse Purpan, Toulouse, France. She was interested in the activation of human lymphoid cells to eradicate cancer cells. Since 2007, she has been a Researcher with the Cancer Research Center of Toulouse, Toulouse, France. Her current research interests are based on the impact of the tumor microenvironment on the survey of cancer cell, particularly in hematopoietic diseases.

Jean-Jacques Fournié received the M.S. and Ph.D. degrees in microbial biochemistry from the University of Toulouse, Toulouse, France, in 1983 and 1986 respectively. From 1988 to 1989, he was a Postdoctoral Fellow with the CIRC (currently the Garvan Institute), Sydney University Australia. In 1986, he joined the National Scientific Research Center (CNRS), Toulouse, France, to study biologically active natural substances with a focus on those activating human cell immunity. In 1990, he settled a cell immunology group focused on nonpeptide antigens, and in 1993, he discovered phosphoT cells, and moved this group to the National antigens stimulating human Institute of Health and Medical Research (INSERM) for pharmacological development of phosphoantigens with therapeutic applications for cancer. In 1999, he cofounded Innate Pharma, which produces new anticancer treatments. Since 2011, he has been heading the Cancer Research Center of Toulouse (CRCT), Toulouse, France. His fields of scientific expertise are biochemistry, pharmacology, immunology, and cancer. The aim of his team is based on the immune argeting of hematopoietic diseases.

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Katia Grenier (S’99–M’03) received the M.S. and Ph.D. degrees in electrical engineering from the University of Toulouse, Toulouse, France, in 1997 and 2000, respectively. She was engaged in microelectromechanical systems (MEMS) circuits on silicon. She was a Postdoctoral Fellow with Agere Systems (Bell Laboratories). In 2001, she joined the Laboratory of Analysis and Architecture of System, National Scientific Research Center (LAAS-CNRS), Toulouse, France. From 2007 to 2009, she was with the Laboratory for Integrated Micromechatronic Systems CNRS (LIMMS-CNRS)/Institute of Industrial Science (IIS), Universtity of Tokyo, Tokyo, Japan, where she was engaged in launching research activities on microwave-based biosensors. Her research interests with LAAS-CNRS are currently focused on the development of fluidic-based microsystems/nanosystems, notably for biological and medical applications at the cellular and molecular levels. Dr. Grenier is a member of the IEEE MTT-10 Technical Committee on Biological Effect and Medical Applications of RF and Microwave of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S).

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An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications Sangkil Kim, Student Member, IEEE, Apostolos Georgiadis, Senior Member, IEEE, Ana Collado, Member, IEEE, and Manos M. Tentzeris, Fellow, IEEE

Abstract—This paper demonstrates the design of an 800-MHz solar-powered active wireless beacon composed of an antenna and an integrated oscillator on a low-cost paper substrate. Inkjet printing is used to fabricate the conductive circuit traces and the folded slot antenna, while the oscillator circuit is designed using off-the-shelf components mounted on the paper substrate. Flexible, low-cost, amorphous silicon (a-Si) solar cells are placed on top of the slot ground and provide autonomous operation of the active circuit eliminating the use of a battery. A prototype is built and characterized in terms of phase noise, radiation patterns, and the effect of solar irradiance. Such low-cost flexible circuits can find significant applications as beacon generator circuits for real-time identification and position purposes, wearable biomonitoring as well as solar-to-wireless power transfer topologies. The measured phase noise is 116 dBc Hz at 1-MHz offset, while drain current is 4 mA and supply voltage is 1.8 V. Index Terms—Active antennas, energy harvesting, flexible electronics, harmonic balance, inkjet printing, solar antenna, wireless beacon, wireless energy transfer, wireless identification.

I. INTRODUCTION

T

HE combination of sensor networks and RF identification (RFID) technologies have spurred numerous applications from logistics and Internet-of-things to monitoring and security, all of which require a capability for large-volume circuit production, as well as the use of low-cost fabrication methods on environmentally friendly flexible substrates, while energy autonomy is critical for operability in rugged environments [1]–[7]. As a result, implementations of flexible passive microwave circuit components, such as antennas, inductors, and transformers, utilizing substrates such as paper, polyethylene Manuscript received July 10, 2012; revised September 23, 2012; accepted September 24, 2012. Date of publication November 16, 2012; date of current version December 13, 2012. The work of S. Kim and M. M. Tentzeris was supported by SRC/IFC and NSF-ECS-0801798. The work of A. Georgiadis and A. Collado was supported by EU COST Action IC0803 (RFCSET) and EU Marie Curie Project FP7-PEOPLE-2009-IAPP 251557. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. S. Kim and M. M. Tentzeris are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30308 USA (e-mail: [email protected]; [email protected]). A. Georgiadis and A. Collado are with the Centre Tecnologic de Telecomunicacions de Catalunya, Castelldefels 08860, Spain (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222922

terephthalate (PET), and textiles are receiving significant attention in the literature [2], [3]. The inkjet printing fabrication process, permitting a large-volume production and allowing a resolution below 50 m, has emerged as a popular alternative to traditional circuit board fabrication techniques, such as chemical etching and milling, finding increasing applicability in the electronics and sensors industries [1], [2]. The possibility of the inkjet printing of a complete system-onsubstrate (SoS), based on multilayer flexible substrate modules and inkjet deposition of active devices remains a challenge, especially when it comes to operating at microwave frequencies. While inkjet printing of semiconducting polymers to develop organic thin-film transistors (OTFTs) [4] is still far from operation in the gigahertz frequency range, integration of off-theshelf active electronic components onto flexible substrates provides an exciting alternative. The realization and integration of active topologies and sensors on flexible substrates, combined with passive interconnects, transmission lines, and antennas, presents a significant challenge with few notable examples in the literature, e.g., [1], [2] and [5]–[7], and presents the object of this study. Furthermore, extending the operational autonomy of wireless sensors and transceivers has spurred significant efforts related to energy harvesting technologies, as well as wireless power transmission [8]. Toward this goal, the objective of this study is the integration of an active circuit with energy harvesting capability on a flexible low-cost paper substrate taking advantage of the capabilities of inkjet printing technology. For benchmarking proof-of-concept purposes, this paper demonstrates a prototype active antenna-based beacon operating at 800 MHz, transmitting power or sending identification information, which is powered by an amorphous silicon (a-Si) solar cell. Such circuits can be utilized as beacon signal generators in potential identification applications, or alternatively, as a solar-to-electromagnetic power converting circuit in wireless power transmission applications. The 800-MHz band is commonly utilized as the primary means of radio communication of data and voice for many city governments, especially for public safety and emergency. The operation frequency of the proposed active antenna can be easily scaled up or down to any other frequency band depending on the application. The use of solar-based electromagnetic signal generation finds direct application in the field of wireless power transmission. Solar energy is captured using solar cells and used to bias a highly efficient oscillator element that will transmit

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its output signal through an antenna element. In order to take advantage of the area that the transmitting antenna elements occupy, the solar cells can be placed sharing the same area of the antenna or even on their ground plane. This way a compact structure that is capable of harvesting solar energy and then use it to transmit electromagnetic signals for wireless power transmission can be obtained. In [9], a solar powered active antenna on a nonflexible Arlon A25N substrate was presented, whereas in [10], a credit-card sized prototype solar powered active antenna on PET was demonstrated. This paper extends previous publications by additionally investigating the effect of solar irradiance on the active antenna performance, enabling the applicability of the proposed beacon to real-world scenaria. The active antenna oscillator is fabricated on a paper substrate with inkjet printing technology and the used solar cells are a-Si solar cells that are also flexible. The combination of paper substrate and flexible a-Si solar cells allow to have a conformal circuit that can be easily integrated in several application scenarios. Furthermore, this paper contains a detailed analysis of the electromagnetic, as well as the nonlinear circuit design, measurements of power gain radiation patterns of the active antenna, and characterization of the active antenna oscillator phase-noise performance. In Sections II and III, design and simulation details of the passive and active antenna (beacon), respectively, are presented. Section IV contains measurements and characterization of the light-powered fabricated integrated prototypes.

and furthermore, the folded slot structure provided sufficient bandwidth. The antenna is the output load of the oscillator, as well as a resonator effectively controlling the oscillation frequency. The broadband folded slot antenna configuration was chosen due to its stable input impedance throughout its operation frequency range, effectively facilitating the design of the oscillator and enhancing its stability. In addition, it is common in wireless modules operating in “rugged” environments that the antenna resonant frequency may shift because of the surrounding environment. The oscillator can be minimally affected by this phenomenon by using a broadband antenna with relatively small input impedance variability contrary to narrowband antennas, such as patch antennas. Additionally, the active antenna will be still able to operate even in the case that the oscillation frequency may vary. Therefore, the proposed active antenna can generate a “stable” power level regardless of the ambient environment, a critical feature in identification and power transmission applications.

II. PASSIVE ANTENNA DESIGN Among the antenna requirements for low-power sensing and beacon applications are: 1) simple layout; 2) ease of integration with solar panels and active circuitry; 3) omnidirectional radiation; 4) frequency tuning capability or broadband performance; and 5) mechanical flexibility. The first requirement allows low-cost large-volume production required for RFID or wireless sensor network applications. Coplanar-waveguide (CPW) technology utilizes only one conductive layer, and therefore it is preferred to microstrip technology in terms of fabrication simplicity. Integration of solar panels with antennas allows for area reduction, and consequently, cost reduction. Slot antennas require a large ground plane, which is advantageous for solar cells, as well as additional circuitry integration. Frequency tuning or broadband characteristic is sought in order to easily reconfigure the antenna to cover different frequency bands depending on geographic location or specific applications. Mechanical flexibility is desired in order to easily place the antenna on different structures. Taking into account the above requirements, a CPW slot antenna topology on a flexible paper substrate was selected. Specifically, a folded CPW slot structure was selected since it provides a greater flexibility to the designer to achieve the desired impedance over a wider frequency range compared to a single slot [11]. In a previous design [9], a grounded folded slot structure was used following [12], which allowed for a slight reduction in antenna size while somewhat reducing bandwidth and antenna efficiency. In this study, the shorting strip was not used, since size reduction was not a critical design goal,

A. Inkjet Printing and Paper Substrate The RF properties of the paper substrate have been thoroughly investigated using the microstrip ring resonators method in [2]. The paper substrate is a very cheap, renewable, and biocompatible material. The dielectric constant of a 0.23-mm-thick Kodak photographic paper is 3.5 at 0.8–1.0 GHz, and the loss tangent is 0.07 through the frequency band of interest [2]. In addition, inkjet-printing technology has lots of advantages in the microwave area. It is a low-cost and an environmentally friendly fabrication process because it only drops the necessary conductive ink on the desired positions. It is different from conventional etching technology, which washes away the unwanted metal creating waste. In this way, circuits can be fabricated using only as much ink as it is required. For the inkjet printing process, the Dimatix DMP2800 inkjet printer,1 and the Dimatix 10 pL cartridge (DMC-11610) were utilized. The angle of the printer head was adjusted to achieve a print resolution of 1270 dots per inch (dpi). The ink that was used for the fabrication was Cabot CCI-300.2 Once the desired pattern is inkjet printed, it needs to be cured in an oven for 4 h at 130 C. The printed silver pattern usually has a dc conductivity in the range from 9 10 S m to 1.1 10 S m with a roughness of about 1 m [13], [14]. The high loss tangent of paper is not important in the proposed design because the paper substrate is very thin thickness of the paper . The magnetic field is generated along the slot and the electric field is built up across the narrow dimensions of the slot. However, the interaction of the electric field with the lossy paper substrate is very small, which results in low substrate loss. Therefore, the conductivity, thickness, and roughness of the metal is more important than the loss of substrate because those are critical factors of conductor loss. Therefore, the high loss of the paper substrate is not a critical design factor for the proposed design. 1[Online]. 2[Online].

Available: http://www.dimatix.com/

Available: http://www.cabot-corp.com/New-Product-Development/Printed-Electronics/Products

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Fig. 1. Folded slot antenna geometry (gap of the CPW line: 0.2 mm).

Fig. 2. Input -parameters of the folded slot antenna.

B. Passive Antenna Design and Measurements In Fig. 1, a photograph of the fabricated passive antenna prototype is presented with the corresponding dimensions. The slot length is 126 mm, and its width is 3.5 mm. The overall length of the antenna is 152 mm, width is 43.2 mm, and thickness of the paper substrate is 228.6 m. The antenna is fed by a CPW line with 5 mm of signal line width and 0.2 mm of ground-to-signal line gap. A full-wave finite-element method (FEM) software tool (Ansys HFSS) is used to design and simulate the passive antenna. Simulated and measured results of the input -parameters of the antenna are presented in Fig. 2, showing a good input impedance match over a bandwidth of approximately 41.5%. The simulated and measured radiation patterns of the antenna at 800 MHz are plotted in Fig. 3, showing a good agreement. The dashed lines in Fig. 3 shows radiation patterns of the passive antenna on the human body. It is noticeable that the gain of the passive antenna is decreased by about 10 dB when it is placed on the body, and an additional 10 dB of the antenna gain is decreased when a radiated wave passes through the human body. The antenna gains in free space and on the human body were evaluated in an outdoor setup and a value of approximately 6 dBi at 960 MHz was measured, as shown in Fig. 4. The gain of the antenna on the human body is about from 5 to 10 dB lower than that of the antenna in free space due to the effect of the lossy human body. The obtained low gain is mainly attributed to the limited dimensions of the ground plane. Fluctuations in the measured gain profile and variation with respect to the simulated values are attributed to the outdoor setup measurement error.

Fig. 3. Radiation patterns at 800 MHz. (a)

-plane. (b)

-plane.

III. ACTIVE ANTENNA OSCILLATOR DESIGN An active oscillator antenna combines an oscillator circuit with a passive radiating structure [15]. It allows for a simple circuit layout, utilizing one active device and a minimum number of passive components, which can be integrated on the antenna structure—in this case, the ground plane surrounding the radiating slot, and thus, permitting a low-profile circuit design. Diodes such as Gunn or impact ionization avalanche transit-time (IMPATT) diodes or transistors such as high electron-mobility transistors (HEMTs) or heterojunction bipolar transistors (HBTs) can be used as the active source for the

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Fig. 4. Simulated and measured passive antenna gain.

oscillator. However, diodes are not suitable for identification and wireless power transmission applications due to their low dc-to-RF efficiency [15], [16]. On the other hand, transistors such as HEMT have high dc-to-RF efficiency, low heat dissipation, and low noise figure, which are critical factors in identification and wireless power transmission applications [15], [16]. In addition, transistors can be easily integrated with planar structures like slot or microstrip antennas [15], [16]. The oscillator circuit was designed using the NE3509M04 pseudomorphic HEMT (pHEMT). A one-stage reflection-type oscillator topology was selected with a simple passive LC tank ( and ). A multistage oscillator or an oscillator with a phase-locked loop (PLL) may increase the frequency stability of the active antenna oscillator; however, such designs lead to an increased circuit complexity and power consumption, which are undesired in beacon circuits for identification and wireless power transfer applications. The circuit schematic of the designed oscillator is shown in Fig. 5. The antenna is connected to the gate terminal of the active device, while a source resistor is used to self-bias the device. Capacitors , , and and inductors and tune the oscillation frequency around 800 MHz. Capacitor provides an RF short and isolates the dc feed from the oscillator circuit. The oscillator was initially designed without the solar cell power supply, using an operating dc power supply (HP/Agilent E3620A) voltage of 1.8 V, and drawing a current of 4 mA. A commercial harmonic-balance simulator (Agilent ADS) was used to simulate the oscillator circuit. A prototype oscillator was built and its performance characterized. The frequency of the oscillator is in good agreement with simulation within an expected yield variation of the off-the-shelf component values (Table I). The oscillation frequency increases with the bias voltage, as shown in Fig. 6(a). Measurement of the oscillator frequency was made by capturing the radiated spectrum of the oscillator using a commercial broadband antenna and a spectrum analyzer. The frequency variation with the bias voltage can be utilized as a frequency-tuning mechanism, or alternatively, it can be minimized by placing a regulator circuit following the dc supply. The fabricated prototype frequency was less sensitive to bias voltage variation than in simulation. This difference can be attributed to yield variations of the used plane components

Fig. 5. Active oscillator antenna. (a) Circuit schematic. (b) Fabricated circuit.

TABLE I CIRCUIT COMPONENT VALUES

and to associated layout parasitics not taken into account in the simulation stage. In addition, the discrepancy of simulation and measurement in Fig. 6(a) also resulted from imperfect modeling of active/passive device like a transistor, inductors, and capacitors. It is because additional parasitic effects such as capacitances and inductances from the surface mount components significantly effect the oscillation frequency of the circuit, and the comparatively low conductivity of inkjet-printed silver trace is also one of the most significant error source. Actual oscillation frequency is lower than the simulated value because the increased resistance and conductor loss cause an additional loading effect beside the unwanted parasitic effect of the transistor. The measured oscillator drain current was approximately 4 mA for bias voltages up to 4.0 V [see Fig. 6(b)]. Correspondingly, the dc power of the oscillator increases from 5.6

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Fig. 6. Active oscillator antenna performance versus dc-bias voltage. (a) Oscillation frequency variation. (b) Current consumption variation.

to 16 mW as the supply voltage ranges from 1.4 to 4.0 V (Fig. 6). The voltage regulator dissipates power about 1.2–8.8 mW as the supply voltage ranges from 2.1–4 V. Measured effective isotropic radiated power (EIRP) (dBm) patterns of the active antenna oscillator are shown in Fig. 7, showing a good agreement with the radiation patterns of the passive antenna as expected. The maximum EIRP on the - and -plane is 22.88 and 25.98 dBm, while the minimum EIRP on both planes is 3.91 and 20.34 dBm, respectively. Fig. 7. Measured EIRP (dBm). (a)

-plane. (b)

-plane.

IV. AUTONOMOUS OPERATION USING SOLAR ENERGY Autonomous operation of the active antenna was achieved by utilizing a-Si solar cells to harvest light energy, as shown in Fig. 8. One of the biggest challenges when integrating solar cells together with antenna elements is to select the optimum placement of the solar cell in order to not degrade the performance of the antenna. It is known in the literature that the solar cells have little effect on the radiation and input impedance characteristics of the antenna when properly placed, such as covering areas where the antenna field distribution is weaker [17]–[19]. Additionally, the solar cells should generate enough power to power the active antenna and the power provided should be stable in order to avoid variations in the oscillation frequency

and also to generate a stable low phase-noise signal. The capacitor is mounted as shown in Fig. 5 to isolate the oscillator circuit from the dc feed and additionally the use of a voltage regulator at the output of the solar cell is considered in order to get a stable power from the solar cells, and consequently obtain a more stable oscillation frequency from the active antenna. An amorphous silicon a-Si solar module (Power Film SP3-37) with a 4.1-V open-circuit voltage and 28-mA short-circuit current under 100 mW cm (1 sun: a unit of power flux from the sun) solar irradiation was used as a dc power supply. The SP3-37 module internally consists of five a-Si solar cells with approximately 0.85-V open-circuit voltage and 28-mA

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Fig. 9. Solar cell versus illuminance.

(short-circuit current) and

(open-circuit voltage)

Fig. 8. Light powered active oscillator antenna. (a) Fabricated prototype. (b) Indoor measurement setup using a halogen lamp to illuminate the solar module.

short-circuit current in a series connection. In this study, one module was cut in two pieces across its long side and the two parts were properly placed on top of the active antenna ground plane and connected electrically in parallel [see Fig. 8(a)]. Each solar cell piece has approximately 4.1-V open-circuit voltage and 14-mA short-circuit current. An equivalent-circuit model of the solar cell consisting of an ideal current source, an ideal diode with saturation current , a parallel resistance , and a series resistance was created in [8] by measuring the dc I–V curve of the cell. The equivalent-circuit model of the combined solar module is shown in Fig. 5, where the parameters of the solar cell model are nA, , and [10]. The active beacon antenna was first characterized in an indoor environment by using a halogen lamp to excite the solar module. A luxometer was used to measure the illuminance at the active antenna position, while the distance of the halogen lamp was varied. Illuminance is typically used to characterize luminous sources at indoor environments. It is a photometric measure, which corresponds to the irradiance weighted by a luminocity function corresponding to the sensitivity of the human eye to light [19]. Solar irradiance of 100 mW cm (1 sun) corresponds to 100 klux illuminance [19]. The measured illuminance at the solar cell location is about 1.8 10 lux, 6 10 lux, and 2 10 lux when its distance from the halogen lamp is 127, 300, and 500 mm, respectively. The solar cell’s short-circuit current and open-circuit voltage depending on illuminance are shown in Fig. 9. It shows that the oscillation

Fig. 10. Oscillation frequency versus illuminance with and without regulator circuit.

frequency can be stabilized by introducing a voltage regulator circuit since it supplies stable dc power to the oscillator. The stable oscillation frequency results in ease of matching between the antenna and oscillator output, as well as due to the broadband property of the antenna. Figs. 6, 9, and 10 show that the oscillation frequency can be stabilized when the illuminance is higher than 3.3 10 lux since the solar cell is able to produce enough power to operate the circuit. The solar cell generates 16.2–28.6 mW depending on illuminance, but the active antenna requires 6–28 mW, which is affordable power from the solar cell providing the illuminace is higher than 3.26 10 lux. The variation of the oscillator frequency with the illuminance is shown in Fig. 10. For illuminance values less than 2 10 lux, it was not possible to power up the oscillator. The frequency of oscillation is reduced compared to Fig. 6 due to the loading effect of the solar modules. The observed frequency variation is also due to the measurement setup as the lamp structure includes a metallic reflector [see Fig. 8(b)] that is affecting the antenna impedance, and subsequently the oscillator frequency. A commercial regulator LT1763-1.8 with 1.8-V output voltage by Linear Technology, Milpitas, CA, was additionally used to minimize the dc

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Fig. 11. Radiation patterns of active antenna oscillator under sun light conditions. (a) -plane. (b) -plane.

supply variation due to the illuminance variation. The dissipated power of the regulator is in the range of 4.05–6.05 mW, including quiescent power when it is powered by the solar cell providing the illuminace is stronger than 3.26 10 lux. Measurements are included in Fig. 10, demonstrating a significantly reduced frequency dependence on the illuminance. It was not possible to properly power the regulator for illuminance values less than 3.26 10 lux. Finally, a slight increase of the oscillating frequency was observed when using the regulator. This is also attributed to the loading effect of the regulator on the active circuit. Radiation patterns of the solar powered active antenna were obtained outdoors at the Georgia Institute of Technology, Atlanta, for a measured illuminance of 1.6 10 lux. The radiated power from the solar-powered active antenna with the regulator circuit is measured, and the measured power patterns are shown in Fig. 11. In order to test the effect of the flexing of the paper substrate on the radiation performance of the autonomous beacon, -plane on-body measurements were also performed by placing the antenna on top of a cotton shirt and at the chest of a person showing an approximately 10-dB reduction in antenna gain (Fig. 11). Similar omnidirectional radiation patterns in free space in Fig. 11 suggest noteworthy results that the solar-powered active antenna has similar radiation patterns to that of the passive antenna. In addition, it loses omnidirectionality when the active antenna is mounted in the human body due to power absorption of the human body since a human body is a very lossy and high dielectric material.

Fig. 12. Measured: (a) power specta and (b) phase noise of active antenna under sun light conditions without/with regulator circuit.

Finally, the power spectrum and the phase noise of the solar powered active antenna was measured. The dashed line in Fig. 12(a) shows the power spectrum of the antenna powered by solar cell without the voltage regulator circuit, while the solid line shows the spectrum of the solar-powered active antenna with the regulator circuit in outdoor environment. It should be noted that solar illuminance with the voltage regulator leads to a cleaner spectrum than the one obtained without the regulator circuit. It is because output voltage of the solar cell is fluctuating depending on an illuminance of the sun. The magnitude difference of the spectra is due to measurement error. The commercial broadband antenna, which have been shown in Fig. 8, cannot be used to get the power spectrum in the outdoor environment because it captures unwanted noises such as TV or other wireless signals too. An open coaxial cable was placed near the antenna to catch a signal from the antenna, which resulted in a magnitude difference of the spectra. The observed frequency shifting of the antenna when it is connected to the regulator is due to loading effect of the regulator circuit, which includes capacitors and the regulator chip. The dashed line in Fig. 12(b) shows the phase noise of the antenna for an illuminance of 1.6 10 lux without the regulator, while the solid line in Fig. 12(b) shows the same measurement by including the regulator circuit. A phase noise value of 116.6 dBc Hz at 1-MHz offset was measured for the circuit that includes the voltage regulator, showing an improvement in the phase noise of around 5 dB due to the better frequency stability when using the voltage regulator. The phase noise of the antenna with the regulator is slightly higher than that of the

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antenna without the regulator at the frequency offset band of 3–4 kHz. It can be considered as an measurement error. This error can be caused due to fluctuation of intensity of sunlight and interference of unwanted signal since the measurement took place in an outdoor environment.

[10] A. Georgiadis, A. Collado, S. Kim, H. Lee, and M. M. Tentzeris, “UHF solar powered active oscillator antenna on low cost flexible substrate for application in wireless identification,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 17–22, 2012, pp. 1–3. [11] H.-S. Tsai and R. A. York, “FDTD analysis of CPW fed folded-slot and multiple-slot antennas on thin substrates,” IEEE Trans. Antennas Propag., vol. 44, no. 2, pp. 217–226, Feb. 1996. [12] R. B. Waterhouse and D. Novak, “Small folded CPW fed slot antennas,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Jul. 9–14, 2006, pp. 2599–2602. [13] S. Kim, Y.-J. Ren, H. Lee, A. Rida, S. Nikolaou, and M. M. Tentzeris, “Monopole antenna with inkjet-printed EBG array on paper substrate for wearable applications,” IEEE Antennas Wireless Propag. Lett., vol. 11, no. , pp. 663–666, 2012. [14] M. L. Allen, M. Aronniemi, T. Mattila, A. Alastalo, K. Ojanpera, M. Suhonen, and H. Seppa, “Electrical sintering of nanoparticle structures,” Nanotechnology, vol. 19, 2008, Art. ID 175201. [15] K. Chang, R. A. York, P. S. Hall, and T. Itoh, “Active integrated antennas,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 937–944, Mar. 2002. [16] H. C. Yen, R. Esfandiari, Y. Hwang, K. Tan, C. Liu, M. Aust, R. Carandang, and H. Wang, “A monolithic approach for -band integrated active phased array transmitting antenna,” in IEEE Antennas Propag. Soc. Int. Symp., Jul. 1992, vol. 1, pp. 126–129. [17] M. Tanaka, Y. Suzuki, K. Araki, and R. Suzuki, “Microstrip antennas with solar cells for microsatellites,” Electron. Lett., vol. 31, pp. 263–266, 1996. [18] S. Vaccaro, J. R. Mosig, and P. de Maagt, “Two advanced solar antenna “SOLANT” designs for satellite and terrestrial communications,” IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 2028–2034, Aug. 2003. [19] A. Virtuani, E. Lotter, and M. Powalla, “Influence of the light source on the low-irradiance performance of Cu(In,Ga)Se2 solar cells,” Solar Energy Mater. Solar Cells, vol. 90, no. 14, pp. 2141–2149, Sep. 2006. [20] A. Georgiadis and A. Collado, “Improving range of passive RFID tags utilizing energy harvesting and high efficiency class-e oscillators,” in 2012 6th Eur. Antennas Propag. Conf., Mar. 26–30, 2012, pp. 3455–3458.

V. CONCLUSION AND FUTURE WORK The fabrication of flexible autonomous sunlight-powered batteryless active beacons on low-cost paper substrates using inkjet printing technology has been demonstrated. An 800-MHz RF prototype integrating an inkjet-printed folded slot antenna and an oscillator with solar cells on paper has verified the unique capabilities of this approach, potentially paving the way for scalable conformal low-cost wireless identification circuits and efficient wireless power transfer topologies. A future challenge toward enabling complete system integration consists of inkjet printing of thin-film energy storage elements such as capacitors and batteries. The next step of this study is to perform an optimized design of the oscillator element in order to maximize its dc-to-RF conversion efficiency by considering class-E topologies for the oscillator element. As one of the targeted applications of the proposed system is wireless power transmission, maximizing the dc to RF efficiency in the oscillator will also maximize the amount of RF power that the system will transmit. In addition, this type of system could be potentially used to increase the range of passive RFIDs. In [20], a similar system was used to increase the range of a passive RFID by, instead of transmitting the signal out of the oscillator, directly feeding it into the RFID. The proposed topology showed an increase in the reading range of the RFID. Based on the same idea as in [20], another potential application is to use the system presented in this paper to transmit RF signals in an RFID environment. The presence of additional RF signals apart from the signals from the reader has shown improvement in the reading range of passive RFIDs. REFERENCES [1] R. Vyas, V. Lakafosis, H. Lee, G. Shaker, L. Yang, G. Orecchini, A. Traille, M. M. Tentzeris, and L. Roselli, “Inkjet printed, self—Powered, wireless sensors for environmental, gas, and authentication-based sensing,” IEEE Sens. J., vol. 11, no. 12, pp. 3139–3152, Dec. 2011. [2] L. Yang, A. Rida, R. Vyas, and M. M. Tentzeris, “RFID tag and RF structures on a paper substrate using inkjet-printing technology,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2894–2901, Dec. 2007. [3] A. Tronquo, H. Rogier, C. Hertleer, and L. Van Langenhove, “Robust planar textile antenna for wireless body LANs operating in 2.45 GHz ISM band,” Electron. Lett., vol. 42, no. 3, pp. 142–143, Feb. 2006. [4] L. Basiricò, P. Cosseddu, B. Fraboni, and A. Bonfiglio, “Inkjet printing of transparent, flexible, organic transistors,” Thin Solid Films, vol. 520, no. 4, pp. 1291–1294, Dec. 2011. [5] A. Rida, L. Yang, R. Vyas, and M. M. Tentzeris, “Conductive inkjetprinted antennas on flexible low-cost paper-based substrates for RFID and WSN applications,” IEEE Antennas Propag. Mag., vol. 51, no. 3, pp. 13–23, Jun. 2009. [6] B. S. Cook and A. Shamim, “Inkjet printing of novel wideband and high gain antennas on low-cost paper substrate,” IEEE Trans. Antennas Propag., vol. 60, no. 9, pp. 4148–4156, Sep. 2012. [7] B. Ando and S. Baglio, “Inkjet-printed sensors: A useful approach for low cost, rapid prototyping,” IEEE Instrum. Meas. Mag., vol. 14, no. 5, pp. 36–40, Oct. 2011. [8] N. Shinohara, “Power without wires,” IEEE Microw. Mag., vol. 12, no. 7, pp. S64–S73, Dec. 2011. [9] F. Giuppi, A. Georgiadis, S. Via, A. Collado, R. Vyas, M. M. Tentzeris, and M. Bozzi, “A 927 MHz solar powered active antenna oscillator beacon signal generator,” in Proc. IEEE Top. Wireless Sensors and Sensor Networks Conf., Santa Clara, CA, Jan. 15–18, 2012, pp. 1–4.

Sangkil Kim (S’12) received the B.S. degree in electrical and electronic engineering from Yonsei University, Seoul, Korea, in 2010, the M.S. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2012, and is currently working toward the Ph.D. degree at the Georgia Institute of Technology. He is currently involved with the design and fabrication of novel wearable electronics for body area networks.

Apostolos Georgiadis (S’94–M’03–SM’08) was born in Thessaloniki, Greece. He received the B.S. degree in physics and M.S. degree in telecommunications from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 1993 and 1996, respectively, and the Ph.D. degree in electrical engineering from the University of Massachusetts at Amherst, in 2002. In 2002, he joined Global Communications Devices (GCD), North Andover MA, as a Systems Engineer, involved with CMOS transceivers for wireless network applications. In June 2003, he joined Bermai Inc., Minnetonka, MN, as an RF/Analog Systems Architect. In 2005, he joined the University of Cantabria, Santander, Spain, as a Juan de la Cierva Fellow Researcher. In March 2007, he joined the Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), Castelldefels, Spain, as a Senior Research Associate in the area of communications subsystems. He serves on the Editorial Board of the Radioengineering Journal. His research interests include energy harvesting, RFID technology, nonlinear microwave circuit design, active antenna arrays, and specifically coupled oscillator arrays. Dr. Georgiadis is the chairman of COST Action IC0803 RF/microwave communication subsystems for emerging wireless technologies (RFCSET). He is the coordinator of Marie Curie Industry–Academia Pathways and Partnerships (IAPP) project Symbiotic Wireless Autonomous Powered System (SWAP). He is a member of the IEEE MTT-S TC-24 RFID Technologies and IEEE MTT-S TC-26 Wireless Energy Transfer and Conversion.

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Ana Collado (M’07) was born in Santander, Spain. She received the B.S. degree in telecommunications engineering and Ph.D. degree from the University of Cantabria, Santander, Spain, in 2002 and 2007, respectively. In 2002, she was with the University of the Basque Country, Bilbao, Spain, where she was involved in the study of the uncertainty in noise-figure measurements in monolithic-microwave integrated-circuit low-noise amplifiers. Since July 2007, she has been a Research Associate with the Centre Tecnològic de Telecomunicacions de Catalunya, Castelldefels, Spain, where she is involved in the area of communication subsystems. Her areas of interest include the development of techniques for practical bifurcation control and stability analysis of power amplifiers and coupled oscillator systems, RFID technology, energy harvesting, and wireless power transmission solutions. Dr. Collado was a 2011 Marie Curie Fellow Researcher for Project EU FP7251557 Symbiotic Wireless Autonomous Powered system (SWAP), and Management Committee Member and Grant Holder Representative of EU COST Action IC0803, RF/microwave communication subsystems for emerging wireless technologies (RFCSET).

Manos M. Tentzeris (S’89–M’92–SM’03–F’10) received the Diploma degree in electrical and computer engineering (magna cum laude) from the National Technical University of Athens, Athens, Greece, and the M.S. and Ph.D. degrees in electrical engineering and computer science from The University of Michigan at Ann Arbor. He is currently a Professor with School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta. He has helped develop academic programs in highly integrated/multilayer packaging for RF and wireless applications using ceramic and organic flexible materials, paper-based RFIDs and sensors, biosensors, wearable electronics, inkjet-printed electronics, “Green” electronics and power scavenging, nanotechnology applications in RF, microwave microelectromechanical systems (MEMs), system-on-package (SOP)-integrated (ultra-wideband (UWB), multiband, millimeter wave, conformal) antennas and adaptive numerical electromagnetics (FDTD, multiresolution algorithms). He heads the ATHENA research group (20 researchers). He is currently the head of the Electromagnetics Technical Interest Group, School of Electrical and Computer Engineering, Georgia Institute of Technology. From 2006 to 2010, he was the Georgia Electronic Design Center Associate Director for RFID/sensors

research. From 2003 to 2006, he was the Georgia Institute of Technology National Science Foundation (NSF) Packaging Research Center Associate Director for RF Research and the RF Alliance Leader. During the summer of 2002, he was a Visiting Professor with the Technical University of Munich, Munich, Germany. During the summer of 2009, he was a Visiting Professor with GTRI-Ireland, Athlone, Ireland. In the summer of 2010, he was a Visiting Professor with LAAS-CNRS, Toulouse, France. He has authored or coauthored over 420 papers in refereed journals and conference proceedings, five books, and 19 book chapters. He is an Associate Editor for the International Journal on Antennas and Propagation. Dr. Tentzeris was the Technical Program Committee (TPC) chair for the 2008 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) and the chair of the 2005 IEEE CEM-TD Workshop. He is the vice-chair of the RF Technical Committee (TC16), IEEE CPMT Society. He is the founder and chair of the RFID Technical Committee (TC24), IEEE MTT-S. He is the secretary/treasurer of the IEEE C-RFID. He is a member of URSI-Commission D and the MTT-15 committee. He is an Associate Member of the European Microwave Association (EuMA). He is a Fellow of the Electromagnetic Academy. He is a member of the Technical Chamber of Greece. He is an IEEE MTT-S Distinguished Microwave Lecturers (2010–2012). He was an associate editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He is an associate editor for the IEEE TRANSACTIONS ON ADVANCED PACKAGING. He has given over 100 invited talks to various universities and companies all over the world. He was the recipient/corecipient of the 2012 FiDiPro Professorship in Finland, the 2010 IEEE Antennas and Propagation Society Piergiorgio L. E. Uslenghi Letters Prize Paper Award, the 2011 International Workshop on Structural Health Monitoring Best Student Paper Award, the 2010 Georgia Institute of Technology Senior Faculty Outstanding Undergraduate Research Mentor Award, the 2009 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES Best Paper Award, the 2009 E. T. S. Walton Award of the Irish Science Foundation, the 2007 IEEE Antennas and Propagation Society (AP-S) Symposium Best Student Paper Award, the 2007 IEEE MTT-S IMS Third Best Student Paper Award, the 2007 ISAP 2007 Poster Presentation Award, the 2006 IEEE MTT-S Outstanding Young Engineer Award, the 2006 Asian–Pacific Microwave Conference Award, the 2004 IEEE TRANSACTIONS ON ADVANCED PACKAGING Commendable Paper Award, the 2003 NASA Godfrey “Art” Anzic Collaborative Distinguished Publication Award, the 2003 IBC International Educator of the Year Award, the 2003 IEEE CPMT Outstanding Young Engineer Award, the 2002 International Conference on Microwave and Millimeter-Wave Technology Best Paper Award, the 2002 Georgia Institute of Technology–Electrical and Computer Engineering Outstanding Junior Faculty Award, the 2001 ACES Conference Best Paper Award, the 2000 National Science Foundation (NSF) CAREER Award, and the 1997 Best Paper Award of the International Hybrid Microelectronics and Packaging Society.

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On the Detection of Frequency-Spectra-Based Chipless RFID Using UWB Impulsed Interrogation Prasanna Kalansuriya, Student Member, IEEE, Nemai Chandra Karmakar, Senior Member, IEEE, and Emanuele Viterbo, Fellow, IEEE

Abstract—A novel approach is presented to accurately estimate the resonant features of a multipatch backscatter-based chipless radio frequency identification (RFID) tag. An ultra-wideband impulse radar (UWB-IR)-based reader interrogates the chipless tag with a UWB pulse, and the received backscatter is analyzed in the time domain. The key components constituting the backscattered signal, the structural mode, and the antenna mode are identified, and their spectral content are analyzed. Analysis shows that the antenna mode backscatter contains the information carrying signal while the structural mode backscatter contains no information about the tag. A semi-analytical model is developed to explain the behavior of the signal backscattered from the chipless RFID tag. Simulation and semi-analytical results are validated by experimental measurements obtained in an anechoic chamber environment using a 4-b multipatch chipless RFID tag. The new method does not rely on calibration tags for operation and has a greater degree of freedom in the orientation of tags with respect to a reader. A novel method, selective spectral interrogation (SSI), that uses a set of interrogation pulses to extract information bits stored in the spectral signature of the chipless tag is also introduced. Index Terms—Backscatter, chipless radio frequency identification (RFID), ultra-wideband impulse radar (UWB-IR), time domain.

I. INTRODUCTION

R

ADIO FREQUENCY identification (RFID) has automated the process of item tracking and data entry involved in a multitude of applications in a diverse set of industries ranging from logistics and inventory management systems to food and agriculture. The fully automatic long-range operation has been the key feature that differentiates RFID from other automatic identification and tagging technologies, such as one-dimensional (1-D) and two-dimensional (2-D) optical barcodes. The advances in semiconductor technology and tag manufacturing technology has enabled mass production of RFID tags at very low costs, as low as 7–15 cents. However, the cost of individual RFID tags are still significant to present

Manuscript received July 10, 2012; revised September 08, 2012; accepted September 13, 2012. Date of publication November 15, 2012; date of current version December 13, 2012. This work was supported in part by the Australian Research Council’s Linkage Project under Grant LP0991435 and Express Promotions Australia Pty Ltd. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with the Department of Electrical and Computer Systems Engineering, Monash University, Clayton, VIC, 3800 Australia (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222920

barriers to entry into applications involving very large-scale item tagging, such as library management systems where optical barcodes are predominately used. Chipless RFID [1] has recently gained much interest as a solution to reduce the costs in mass deployment of RFID technology. The conventional passive RFID consists of an antenna for harvesting energy from the signals transmitted by an RFID reader and an integrated electronic circuit or chip that assists in the wireless communication process. The chip also contains an electronic product code (EPC) that is transmitted back to the reader by the chip through digital remodulation of the reader signal. On the other hand, a chipless RFID tag contains no electronic circuitry and is void of any capacity for intelligent signal processing, which makes it less expensive and easily mass produced at a unit cost comparable to optical barcodes. It is therefore, essentially the RF counterpart of an ordinary optical barcode. Research on chipless RFID tags can be broadly classified into two main categories: time-domain reflectometry (TDR)-based chipless RFID and frequency-signature-based chipless RFID. In TDR-based tags, the RFID reader transmits an ultra-wideband (UWB) RF interrogation pulse and listens to the reflections or echoes coming back from the tag [2]–[7]. By varying the structural properties of the tag, the time of arrival of these echoes can be controlled, providing a method for passive data storage in the tag. In frequency-signature-based chipless RFID tags [8]–[10], the frequency spectrum of the interrogation signal sent by the RFID reader is transformed by the tag to represent data bits. Most of the research on these frequency signature or frequency-spectra-based tags use planar microwave circuits to realize these transformations in the amplitude or phase spectra of the backscattered signals. Frequency-spectra-based RFID systems and TDR-based RFID systems have their own advantages and disadvantages. The operation of TDR-based chipless RFID systems inherently requires the use of a UWB impulse radar (UWB-IR)-based reader architecture [6], [7]. This is because the interrogation of the tag is done by using an extremely short-duration (lasting only a few hundred picoseconds) broadband RF pulse. This IR-based reader architecture provides a low-cost means for reader design, as opposed to the frequency-modulated continuous-wave (FMCW)-based readers [8], [11] used for reading frequency-spectra-based chipless RFID tags, which require expensive wideband voltage-controlled oscillators (VCOs). From the work reported in literature, it is generally observed that more information can be stored in frequency-spectra-based chipless tags [12], [13] than in TDR-based tags. However, TDR-based chipless tags have a greater degree of freedom in

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positioning the tag with respect to the reader [14] and can be detected successfully up to several meters [6]. Also, they do not require the use of calibration tags or calibration ground planes that need to be placed at the tag location in order to obtain reference measurements as in [8] and [15]. The use of UWB-IR-based interrogation for frequencyspectra-based chipless RFID has not received much attention [15]–[17]. By using UWB-IR-based interrogation of frequency-spectra-based chipless RFID and analyzing the backscatter in the time domain, it is possible to combine the benefits of both classes of chipless RFID systems. This will give rise to the development of chipless RFID operating at longer ranges with a higher data capacity and that are less constrained on positioning, orientation, and calibration requirements. The authors of [15] use the singularity expansion method to characterize the response of a chipless RFID tag to an RF impulse. The response is expressed using a set of poles and residues that are in turn used in the representation of the information encoded in the chipless RFID tag. The proposed technique is experimentally verified. However, reading the tag involves in a three-step measurement procedure: 1) a first calibration measurement in an empty room; 2) a second calibration measurement with a ground plane placed at the location of the tag; and 3) the tag measurement. Therefore, it is not suitable for an application where the distance to the tag varies or where the environment is highly dynamic. In [16], UWB pulsed interrogation of a spiral resonator-based chipless RFID is considered where a meandering transmission line is used to isolate and show that the resonance information of the spirals is contained in the antenna mode of the backscatter. The research detailed in [17] analyzes the backscatter from a multipatch-based chipless RFID tag that is read using a UWB-IR-based reader. In both [16] and [17], the proposed methods do not require a calibration tag to aid the detection process and solely relies on the backscattered signal to estimate the resonance information of the tag. However, the methods are not validated using experimental results and are based only on electromagnetic simulations. In this paper, we explore the use of UWB impulse-based interrogation for remotely estimating the resonant features of a backscatter-based multipatch chipless RFID tag as in [17]. We extend and validate the work reported in [17] through further analysis and by using experimental results. The proposed system uses a single antenna configuration for interrogating the tag and receiving its backscatter. The single-antenna arrangement provides a wider degree of freedom in orienting the tag with respect to the reader. It is shown that the resonant information of the chipless tag is contained only in the antenna mode of the backscatter using electromagnetic simulation results. A mathematical model based on semi-analytical approximations is also derived to explain the behavior of the backscatter and to show how the individual components of the system contribute to the formation of the total received signal. The simulation and analytical results are also validated by measurement results obtained through experiments conducted in an anechoic chamber environment. The operation of the proposed system does not require calibration ground planes or calibration tags, and the new method gives acceptable performance under different tag orientations and positions with respect to the reader location. Finally, a novel detection method called selective spectral interrogation

Fig. 1. Multipatch chipless RFID tag and reader system.

(SSI) is introduced in order to accurately detect the information stored in the chipless tag amidst false spectral peaks caused by noise and clutter. The method uses a set of interrogation pulses, where each pulse is designed to maximize a unique resonance of the tag. It is shown that, by employing a peak detection algorithm together with these interrogation pulses, it is possible to accurately extract the information contained in the frequency spectrum of the chipless tag. The remainder of this paper is organized as follows. Section II describes the chipless RFID system model considered in the paper. Section III presents the electromagnetic simulation results and analyzes the key components of the signal received at the RFID reader. The derivation of a semi-analytical approximation that explains the behavior of the tag backscatter is presented in Section IV. Experimental validation of the chipless RFID system and the performance of the chipless RFID tag through measurement results are discussed in Section V. Section VI details the representation of digital data in the tag frequency spectrum and provides a detection algorithm to extract the encoded information bits from the chipless tag. Finally, conclusions are drawn in Section VII. II. SYSTEM MODEL Here, the system model of the chipless RFID system is discussed. An overview of the backscattering process is also detailed, and the major components of the backscattered signal are introduced. Fig. 1 illustrates the RFID system considered in this analysis. The RFID reader consists of a single antenna serving as both a inset-fed mitransmitter and a receiver. The tag consists of crostrip patch antennas each resonating at a distinct frequency , where . The signal is the UWB impulse used for interrogating the chipless RFID tag. The total received consists of three components signal (1) is the rejecThe largest and the first received component due to the return loss profile of the tion of the transmit pulse antenna. The transients of gradually decay down to zero. At this moment in time, the reader antenna has fully transmitted and is receptive to any backscatter coming from the tag. is the structural mode of The second component received the backscatter. This is followed by the antenna mode of the , which is the weakest and the last component backscatter to be received [18], [19]. Let be the return loss profile of the antenna. From the definition of the return loss, the rejected

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of the pulse input into the antenna can be written (2)

where denotes the inverse Fourier transform. Throughout the paper, we will use lower case letters to denote time-domain signals and the upper case letters to denote . the respective frequency-domain signal, i.e., Due to the presence of a tag in front of the transmit/receive , slightly antenna, the original return loss of the antenna, changes. The return loss of the antenna is affected by the backscatter incident on the antenna and is considered to be electromagnetically loaded by the chipless tag. Let be the modified or affected return loss of the antenna. Using , (1) can be rewritten as

Fig. 2. (a) UWB interrogation pulse shape. (b) Frequency spectrum of pulse.

(3) and , From (1)–(3), we can write an expression for which introduces the electromagnetic loading in the reader antenna, as follows: (4) Equation (4) is particularly useful in calculating the time-domain backscatter from the frequency-domain antenna return loss measurements taken using a vector network analyzer (VNA). Section V will discuss in detail the experimental validation of the system. III. SYSTEM VALIDATION USING ELECTROMAGNETIC SIMULATION Here, we present the operation of the chipless RFID system using electromagnetic simulation results. Here, the frequency spectra of the key components making up the backscatter are analyzed. In order to obtain a backscattered signal close to realistic conditions, the entire system shown in Fig. 1 was constructed in CST Microwave Studio [20] as a three-dimensional (3-D) model, and full-wave electromagnetic simulation was performed.

Fig. 3. (a) Chipless tag consisting of four inset-fed patch antennas resonating at four distinct frequencies. The dimension of a patch determines its resonant and frequency. The design used a substrate of Taconic TLX-8 with characteristics of each patch antenna. thickness 0.5 mm. (b)

A. UWB Transmission

B. Tag Design and Operation

The UWB pulse used in the simulation is a modulated Gaussian pulse having a 20-dB bandwidth of 6 GHz spanning from 2 to 8 GHz. The transmitted interrogation pulse can be expressed as

Fig. 3 shows the tag used in this paper. The tag considered in this work is similar to that in [9] and consists of an array of four inset-fed microstrip patch antennas. Each individual patch antenna is a half-wavelength resonator that resonates at a distinct frequency. By varying the dimensions of the patches, the tag can be engineered to have a unique spectral signature or a transfer function characterized by a set of resonances. This signature can be used to store information. The tag shown in Fig. 3 consists of four square patch antennas, having widths of 20, 18, 16, and 15 mm, which resonate at 4.64, 5.16, 5.8, and 6.2 GHz, respectively. The patches also have directive radiation patterns, where the 20-, 18-, 16-, and 15-mm patches respectively show 8, 8.2, 8.7, and 8.2 dBi of directivity. In this work, we focus on the amplitude spectrum as opposed to the phase spectrum as in [9]. When the transmitted UWB pulse interacts with the

(5) where 0.6 ns and 0.114 ns are the parameters defining and the shape of the envelope Gaussian pulse, and GHz are, respectively, the amplitude and the frequency of the sinusoidal carrier signal. Fig. 2(a) shows the shape of the transmitted pulse, and Fig. 2(b) shows its frequency spectrum. The pulse is transmitted using a coplanar waveguide (CPW)-fed circular disc loaded monopole antenna that operates from 2 to 7.3 GHz.

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and . The amplitude Fig. 5. Normalized amplitude spectrum of has a Gaussian shape similar to the input pulse whereas the spectrum of shows four spectral peaks corresponding to the four resonant spectrum of frequencies of the patch antennas in the tag.

Fig. 4. (a) Complete received signal showing and . of

at the antenna (b) Enlarged portion

tag, part of it is harnessed by the individual patch antennas constituting the tag and another part of it is immediately reflected. is caused by the size and shape of the The initial reflection metallic structure of the tag irrespective of the resonant properties of the tag patch antennas and is termed the structural mode of the backscatter [18]. Following this initial backscatter is a , which is made secondary backscatter, the antenna mode up of the signals captured by the individual patch antennas at their respective resonant frequencies. The strength of this reradiated signal is determined by the loading condition of each patch antenna. In this work, we have considered an open-circuit loading condition to maximize the antenna mode backscatter. C. Analysis of Tag Backscatter when the tag Fig. 4 shows the complete received signal is placed 30 cm away from the reader antenna. Once the initial rejection has faded away, it is clearly observed that the reader antenna picks up the backscatter from the tag after a propagation delay of 2.55 ns. The backscatter consists of a larger component followed by transients. We hypothesize that the larger component is the structural mode , and the transients make up the . However, since there is no transmission line between the patch antennas and their open circuited termination as in [14], it is difficult to clearly define where ends and starts. Fig. 5 shows the spectral content of the windowed structural mode and windowed antenna mode obtained using the discrete Fourier transform (DFT). The DFT was computed using the fast Fourier transform (FFT) algorithm. A raised cosine window was used to approximately window out and . It is clear that , which is the larger and first

portion of the backscatter, has a Gaussian amplitude spectrum similar to the spectrum of the transmitted UWB pulse [refer to Fig. 2(b)] and does not contain any information of the resonant frequencies of the tag. On the other hand, the spectral content of the windowed clearly reveals the four resonant frequencies ( 4.6, 5.1, 5.7, and 6.1 GHz) of the individual patch antennas. Therefore, it is clear that the transients following the initial strong backscatter holds the information required to estimate the resonant frequencies of the patch antennas in the chipless tag. It is also observed that the height of the peaks corresponding to the resonances closely follow a contour of a Gaussian amplitude spectrum. This is partly because the amplitude spectra of the transmitted pulse is Gaussian as seen in Fig. 2(b). The antenna mode simply consists of a filtered version of the transmitted signal where signals corresponding to the resonances will only be present. IV. SEMI-ANALYTICAL APPROXIMATION BACKSCATTER

FOR

TAG

The full-wave electromagnetic simulation performed using CST Microwave Studio provides a very accurate and realistic result. However, it does not provide insight into how the different components of the system contribute to produce the final result. Also, if a small change is made to the system, in order to understand its effect, the whole system needs to be resimulated. This is not desirable since full-wave electromagnetic simulation using CST consumes a large amount of computational resources and time. Here, we present the derivation of a simplified mathematical model for describing the backscatter from the tag. The model approximates the entities (e.g., reader antenna, wireless channel, and patch antennas of the tag) constituting the total system as linear time-invariant (LTI) subsystems [21] that can each be fully described using a specific transfer function. The model developed here requires the knowledge of the return loss profiles of the reader antennas and the patch antennas of the tag, which are usually known beforehand or can be easily obtained through measurement or simulation. Therefore, it is not a complete analytical solution but a semi-analytical approximation. It is presented to validate and augment the intuitive discussion presented in Section III. Furthermore, it is capable of providing a reasonably accurate solution very quickly with reasonably low computational requirements. In this model, we assume that the tag and the reader antenna are perfectly polarization matched.

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A. Structural Mode of Tag Backscatter In this approximation, we model the structural mode of the backscatter as a signal that simply gets reflected off of a reflective surface, where the spectral content of the reflected signal is not altered. Here, the structural mode backscatter is simply an attenuated version of the signal that is emitted by the reader antenna into the free space, which is in turn picked up by the same antenna after a propagation delay through the can be written as (refer to wireless channel. Therefore, Appendix A for derivation)

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are terminated with an open circuit (refer to Section III-B), the received signals experience a large mismatch at this termination point. This causes these signals to be reflected once they have reached the termination and get retransmitted back through the patch antennas causing a secondary backscatter (antenna mode) that follows the initial structural mode. Since the chipless tag consists of multiple patch antennas, each individual patch antenna will contribute to the formation of the total antenna mode as backscatter. Hence, we can write (9)

(6) and account for the antenna gain and other losses where associated with the transmission and reception of signals, respectively. Since the same antenna is used for both transmission . The factor accounts and reception, we have for the amount of signal reflected back towards the reader due to is the forward wireless channel, the reflection at the tag, is the backward wireless channel, and accounts for the effective antenna aperture. Here, the signal being emitted into the wireless medium by the antenna is approximated to be . When (6) is inspected from proportional to left to right, it simply expresses how the signal injected into , propagates through the total the reader transmit antenna, , that is, the signal injected to the reader system to produce is emitted by the antenna, propagates through the antenna , reaches the tag and gets reforward wireless channel flected with some loss, propagates back through the backward , and is received by the same antenna. wireless channel We assume that the wireless channel between the transmit antenna and the tag is free of multipath propagation and that there exists a direct unobstructed line of sight path between them. Hence, the effect of the wireless channel constitutes simply to an attenuation due to the path loss and a propagation delay of , where is the speed of light and is the distance between the reader antenna and tag. Since both forward and backward wireless channels are identical we have (7) The effective aperture of an antenna is defined as when considering a transmission power-based analysis [18]. However, since we are considering the voltage in this analysis, the transfer function was defined to capture the effect of the effective antenna aperture as follows:

is the antenna mode backscatter due to the th patch where , having patch anantenna of the chipless tag, can be written as tennas. Similar to (6), an expression for follows:

(10) accounts for the antenna gain and other where losses associated with the th patch antenna of the tag, and and are, respectively, the return loss profile and the load reflection coefficient of the th patch antenna. Similar accounts for the effect of to (8), the transfer function the effective antenna aperture of the th patch antenna and is defined as follows: (11) where and are the bandwidth and center frequency of the th patch antenna, respectively. A general expression for can be written as [6] (12) In this work, the individual patch antennas are terminated . The propagation delay abruptly using an open circuit from the point where the radiation is picked up by the antenna to the point of termination is defined by . C. Total Received Signal Using (1), (2), and (9), the Fourier transform of the total received signal can be written as

(8) where is the bandwidth of the antenna, is the center freis the rect function [22], [23]. quency of the antenna, and can be calBy taking the inverse Fourier transform of (6), culated. B. Antenna Mode of Tag Backscatter The antenna mode of the backscatter results from the signals that are harvested or received by the individual patch antennas of the multipatch chipless RFID tag. Since these patch antennas

(13) An approximation for can be obtained by substituting for and using (6) and (10). The received time-domain can be approximated by taking the inverse Fourier signal transform of (13). D. Results Based on Semi-Analytical Model Using (13) and substituting for the return loss profiles of the reader’s transmit/receive antenna and the tag’s patch antennas

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Fig. 6. (a) Normalized amplitude spectrum of . spectrum of

(b) Normalized amplitude

using the simulated obtained through CST, an approximation for the total received signal in the time domain was obtained. The structural mode and the antenna mode of the backscatter were windowed using a raised cosine window as in Section III-C. The spectral content of the antenna mode and the structural mode is shown in Fig. 6(a) and (b), respectively. There is a close agreement between the CST results and the results obtained through the semi-analytical approximation where four distinct peaks in the spectral signature are clearly visible at the resonance frequencies of the four tag patch antennas. V. EXPERIMENTAL VALIDATION Here, we will discuss the experimental validation of the simulation results observed previously. For this purpose, experiments were performed in an anechoic chamber enviroment. The experiments were conducted using a vector network analyzer (Agilent PNA E8361A) where the measurements were taken in the frequency domain. These measured data were then converted to the time domain using signal-processing techniques. A. Transmit/Receiving Reader Antenna and Chipless RFID Tag The interrogation signals were transmitted and received by the reader using a single monopole antenna. Fig. 7(a) shows the antenna used for the experiment. It is a CPW-fed circular disc loaded monopole antenna with a 0.3-mm gap between the CPW feed line and the ground. The reader antenna was fabricated on a Taconic TLX-8 substrate material having thickness of 0.5 mm with copper cladding thickness of 17 m. The measured return loss and the E-field radiation patterns for the antenna are shown in Fig. 8(a) and (b), respectively. The antenna performs well from 1.5 to 5 GHz. The return loss profile degrades after 5 GHz. The radiation pattern is omnidirectional for lower frequencies and becomes directive at higher frequencies. The chipless RFID tag used in the experiment is shown in Fig. 7(b). Its operation is explained in detail in Section III-B.

Fig. 7. (a) Transmit/receive antenna: coplanar circular disc loaded monopole antenna. (b) Chipless RFID tag consisting of four inset-fed square patches. Both antenna and tag are fabricated on Taconic TLX-8 having a substrate thickness of 0.5 mm, copper thickness of 17 m, and dielectric constant of 2.55. The gap between the feed line and the ground of the antenna is 0.3 mm.

B. Measurement Setup and Results Measurements were taken in an anechoic chamber where a single-port measurement was carried out using a VNA with a transmission power of 1 mW. Fig. 9 shows the placement of the tag and the reader antenna inside the chamber. The experiment involves two steps. First, the loaded return loss profile of the antenna, , was measured where the presence of the tag affects the return loss profile of the reader antenna. Next, the unloaded return loss of the antenna was measured with an empty chamber without the tag. By applying (4) in Section II to these experimental frequency-domain measurements, the time-domain backscatter from the tag was obtained. Using a raised cosine window, the signals and are windowed as described in Section III-C. The amplitude spectra of these windowed and are shown in Fig. 6, where the chipless tag was placed 30 cm away from the reader antenna in the measurement setup shown in Fig. 9. It is clear that the measurement results are in accordance with the simulation results and the semi-analytical results. It should be noted that the results obtained did not rely on the use of a calibration tag. C. Tag Performance in Different Orientations The performance of the proposed technique was tested experimentally where the tag was placed in different orientations and locations with respect to the reader antenna. Fig. 10 shows the frequency spectra of chipless tags having different combinations of resonant patch antennas ( 4.6 GHz, 5.1 GHz, 5.8 GHz, and 6.2 GHz). The result confirms that the presence of a resonant patch antenna in the chipless tag causes a corresponding peak in the spectral signature of the chipless tag. The performance of the chipless RFID system at different distances is shown in Fig. 11. A tag having resonant patch antennas at frequencies and was positioned at 15, 30, and 50 cm away from the reader antenna. The amplitude

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Fig. 8. (a) Normalized measured E-field radiation pattern of antenna. (b) Measured return loss of antenna.

Fig. 9. Experimental setup for testing chipless RFID system in anechoic chamber environment.

spectrum of the antenna mode backscatter for the different distances is shown in the figure where the amplitudes are normalized with respect to the maximum amplitude registered with the 15-cm measurement. It is clearly observed that the amplitude of the spectrum reduces as the distance increases whereas the shape is preserved. In all three measurements, two distinct spectral peaks are clearly visible at the resonance frequencies and . It is also observed that, as the distance increases, the signal-to-noise ratio (SNR) degrades, which causes ambiguity in the detection of resonant peaks in the spectral signature at higher frequencies particularly with the 50 cm reading. The tag was rotated about its axis of symmetry as shown in Fig. 12(a). The rotation was done about the -axis such that the patch antennas corresponding to the higher frequencies would move away from the reader antenna while the patch antennas corresponding to lower frequencies would move toward the

Fig. 10. Frequency spectra of different chipless tags placed 30 cm in front of the reader antenna.

reader antenna. Fig. 13 shows the estimated tag frequency spectra when the tag is rotated. The tag contained resonant patch antennas at , and , where it was placed 30 cm in front of the reader antenna. It is clear from the results that for rotations less than 45 the spectral signature of the chipless tag can be estimated using the proposed technique without any additional signal processing. All three resonant frequencies of the tag can be clearly distinguished. However, when the tag is rotated beyond 45 the performance degrades and some of the higher resonant frequencies do not appear in the estimated frequency spectra. Since the tag consists of microstrip patch antennas, it has a fairly directive radiation pattern (ranging from 8 to 8.7 dBi). As illustrated in Fig. 12(b), when the tag rotates about the -axis, the main lobe of its radiation pattern faces away from the reader antenna. Therefore, the amplitude of the antenna mode frequency spectra gradually reduces as the tag is rotated. We

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Fig. 11. Frequency spectra of a tag with resonant patch antennas at frequencies and placed at different distances from the reader antenna. All of the amplitudes are normalized with respect to the maximum amplitude of the antenna 15-cm measurement. mode observed with the

Fig. 13. Frequency spectra of a tag having resonances , and placed 30 cm away from the reader antenna. The tag is rotated about itself (about the -axis) at different angles. The amplitude is normalized with respect to the maximum amplitude of the amplitude spectrum obtained for the unrotated or 0 position.

sufficiently large guard band (200 MHz) is utilized between the resonant frequencies, the effect of this shift on the detection performance can be minimized to some extent. VI. DATA REPRESENTATION AND DETECTION Here, we discuss the representation of digital information using the spectral content of the antenna mode backscatter and on the detection of information bits contained in the backscatter of a chipless tag. A. Data Representation

Fig. 12. (a) Perspective view of the position of the tag with respect to the reader antenna. (b) View of the – plane, showing the radiation patterns of the tag and the reader antenna.

From the measurement results presented in the previous section, it is clear that the proposed method of analyzing the spectral content of the windowed antenna mode backscatter reveals the resonant features of the chipless RFID tag. With the prototype tag consisting of four distinct patch antennas, it is possible to encode four data bits where the presence of a patch represents a “1” bit and its absence signifies a “0” bit, that is, we consider a resonant peak observed in the frequency spectrum of the antenna mode backscatter to denote a logic “1.” If we encode the and the most significant bit (MSB) as the lowest frequency least significant bit (LSB) as the highest frequency , then all of the spectral signatures shown in Fig. 11 encode the data “1010.” B. Detection of Information Bits

hypothesize that the amplitude spectrum of the antenna mode does not experience a large change when the rotation angle is such that ( , 30 ), the portion of the tag radiation pattern directed towards the reader antenna is still within the half-power beam-width (HPBW) of the tag radiation pattern. However, as soon as exceeds this threshold (HPBW/2), the observed spectrum will be severely affected. Due to the tag rotation, a frequency shift is also observed in the spectral peaks, particularly in the peak corresponding to . We speculate that this is a result of the complex interaction of both the rotation of the main radiation lobe of the tag, as mentioned earlier, and the directive radiation pattern of the reader antenna at higher frequencies as shown in Fig. 8(a). When a

From the results shown in Section V, we can observe that, when the distance to the tag increases or when the tag is rotated, the amplitudes of the resonant peaks reduces and the SNR reduces. Therefore, the detection of these peaks is not that obvious, and false peaks due to noise and clutter introduce ambiguity in the detection process. The use of a fixed threshold based detection scheme as in [8] is not justifiable in this context. This is because the amplitude spectrum of the interrogation is not uniform; the center frequencies have higher pulse amplitudes while the lower and higher frequencies have very low amplitudes due to the Gaussian-shaped amplitude spectrum. Therefore, additional signal processing is required for the accurate detection of the information contained in the spectral signature of the chipless tag. For this purpose, we propose a

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Fig. 14. Amplitude spectra of the set of pulses

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novel technique, selective spectral interrogation (SSI), for detection which is based on using a set of interrogation pulses, defined as follows: (14) 0.6 ns, and 0.3 ns. where Here, the carrier frequency of the modulated Gaussian pulse is chosen to be the resonance frequencies of the patch antennas . The parameter of the Gaussian pulse is larger than that of (5), which makes this pulse less broadband with more energy concentrated around . The premise behind the operation of this method is as follows. When the tag is in, if the tag contains a resterrogated with the pulse onant patch antenna at , then the amplitude spectrum of the antenna mode backscatter should show a spectral peak at . This peak will be considerably larger than all of the other peaks corresponding to the other resonance frequencies of the tag or contains false peaks due to noise. This is because the pulse more energy near than all of the other resonance frequencies, to be more prominent if hence causing the tag resonance at it exists. If such a maxima in the amplitude spectrum is not observed, then it implies that the tag does not contain the patch antenna resonating at . Fig. 14 shows amplitude spectra of the four different interrogation pulses . The 20-dB bandwidth of these pulses are approximately 2.2 GHz. By substiwith in (4), the backscatter response from tuting can be the tag when the tag is interrogated using the pulse data. calculated from the measured Fig. 15 shows the frequency spectrum of the windowed antenna mode backscatter when a tag having patch antennas res. The onating at and was interrogated using the pulses tag was placed 50 cm away from the reader antenna [Fig. 11(c) shows the frequency spectrum of this tag when interrogated using the UWB pulse defined in (5)]. From the figure, it is clear and are used to interrogate the tag, the that, when maximum amplitude occurs at the corresponding resonance freand quencies of and , whereas, when the pulses are used, the maximum amplitude does not occur at the respective resonances of and . This confirms that the tag does not and . Therecontain the patch antennas that resonate at fore, the information contained in the tag is correctly detected as “1010.” The frequency spectra of the antenna mode backscatter obtained for a tag having patch antennas resonating at and is

Fig. 15. Amplitude spectrum of the windowed antenna mode backscatter for . The tag measured contained patch antennas resonating at different pulses and (tag carried data “1010”) and was placed 50 cm away from the reader antenna.

Fig. 16. Amplitude spectrum of the windowed antenna mode backscatter for . The tag measured contained patch antennas resonating at different pulses and (tag carried data “1001”) and was placed 30 cm away from the reader antenna.

shown in Fig. 16. Here, when the pulses and are used, the maximum amplitude does not occur at and , which confirms that neither of these resonances are present in the tag. Hence, the information contained in the tag can be correctly detected as “1001.” It is clear that, by using the SSI method, the data contained in the amplitude spectrum of the antenna mode backscatter can be extracted using a peak detection algorithm. The performance of this algorithm can be further enhanced by supplementing the

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peak detection with an energy computation metric that provides the energy at the vicinity of each resonance frequency. VII. CONCLUSION In this paper, a new method is proposed to accurately estimate the resonant features of a multipatch frequency-spectra-based chipless RFID tag. A UWB-IR-based reader architecture is used to interrogate the tag, where the backscatter is analyzed in the time domain. Through electromagnetic simulations, it is shown that the information-carrying component of the received signal is contained in the antenna mode of the backscatter, whereas the structural mode of the backscatter contains no information about the resonant properties of the chipless tag. A semi-analytical approximation is also derived to explain the nature of the backscattered signal and to provide insight on how each and every individual component of the system contributes to the total received signal at the reader. The results obtained from simulations and the semi-analytical approximation are also validated by measurement results obtained through experiments conducted in an anechoic chamber environment. The proposed method is capable of successfully estimating the resonant properties of a chipless tag without using calibration tags and additional signal processing up to a distance of 30 cm. Also, the effects of tag orientation and location with respect to the reader on the estimation of the tag frequency spectra is investigated. It is shown that, for tag rotations less than 45 , the estimated frequency spectra is usable for detecting the information contained in it. A novel detection method is introduced to perform detection of the spectral peaks amidst false peaks due to noise and clutter. The method uses the tag responses obtained for a set of interrogation pulses and a peak searching algorithm. It is shown that, by applying the new method on the measured data, it is possible to enhance the read range of a tag up to 50 cm.

no resonant properties. Therefore, it does not give rise to an antenna mode, , where the lossy reflection received by which the antenna consists of only the structural mode is simply an attenuated and delayed version of the signal being transmitted. By taking the square root of (15), we can obtain the , when magnitude of the voltage induced at the receiver, is transmitted as follows:

(16) where is the characteristic impedance of the antenna. Equation (16) only gives the magnitude of the induced voltage at the antenna terminals. By including the propagation delay introduced to the signal when it is propagating through the forward and backward wireless channels, a part of the phase information contained in can be restored as

(17) However, (17) serves only as an approximation because it newhen glects the phase transformations introduced due to the signal is being transmitted and received via the antenna. Equation (17) can be rewritten as

APPENDIX

(18)

Here, we present the derivation of the semi-analytical approx. First, consider the radar range equation for a imation for bi-static radar given in [18, (2)–(125)]:

(15)

where , and . The term due to the effective aperture of the receive an, which is defined in (8). tenna is captured by the function This function simply captures the effect of the effective antenna aperture for the entire bandwidth of operation of the antenna. REFERENCES

and are the received and transmitted power, rewhere is the return loss of the transmitting antenna, spectively, is the return loss of the receiving antenna, and are the losses associated with transmission and reception, reis the directivity of the transmit antenna, spectively, is the directivity of the receiving antenna, is the is the disdistance from the transmit antenna to the target, tance from the target to the receiving antenna, is the wavelength, and is the radar cross section of the target being considered. We assume that there is no polarization mismatches between the antennas. In the case of the chipless RFID system shown in Fig. 1 the same antenna serves as both the transmitting , and receving antenna. Therefore, we have and . For the purpose of deriving an expression we consider the tag to be a metallic object having for

[1] S. Preradovic and N. C. Karmakar, “Chipless RFID: Bar code of the future,” IEEE Microw. Mag., vol. 11, no. 7, pp. 87–97, Dec. 2010. [2] L. Zhang, S. Rodriguez, H. Tenhunen, and L.-R. Zheng, “An innovative fully printable RFID technology based on high speed time-domain reflections,” in Proc. Conf. HDP, Jun. 2006, pp. 166–170. [3] A. Chamarti and K. Varahramyan, “Transmission delay line based ID generation circuit for RFID applications,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 11, pp. 588–590, Nov. 2006. [4] L. Zheng, S. Rodriguez, L. Zhang, B. Shao, and L.-R. Zheng, “Design and implementation of a fully reconfigurable chipless RFID tag using inkjet printing technology,” in Proc. IEEE Int. Symp. Circuits Syst., May 2008, pp. 1524–1527. [5] B. Shao, Q. Chen, Y. Amin, S. M. David, R. Liu, and L.-R. Zheng, “An ultra-low-cost RFID tag with 1.67 gbps data rate by ink-jet printing on paper substrate,” in Proc. IEEE Asian Solid State Circuits Conf., Nov. 2010, pp. 1–4. [6] A. Lazaro, A. Ramos, D. Girbau, and R. Villarino, “Chipless UWB RFID tag detection using continuous wavelet transform,” IEEE Antennas Wireless Propagat. Lett., vol. 10, pp. 520–523, 2011.

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[7] A. Ramos, D. Girbau, A. Lazaro, and S. Rima, “IR-UWB radar system and tag design for time-coded chipless RFID,” in Proc. 6th Eur. Conf. Antennas and Propagation, Mar. 2012, pp. 2491–2494. [8] S. Preradovic and N. C. Karmakar, “Design of short range chipless RFID reader prototype,” in Proc. 5th Int. Conf. Intell. Sensors, Sensor Networks and Inf. Process., Melbourne, Australia, Dec. 2009, pp. 307–312. [9] I. Balbin and N. C. Karmakar, “Phase-encoded chipless RFID transponder for large-scale low-cost applications,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 8, pp. 509–511, July 2009. [10] P. Kalansuriya, N. Karmakar, and E. Viterbo, “Signal space representation of chipless RFID tag frequency signatures,” in Proc. IEEE Global Telecommun. Conf., Houston, TX, Dec. 2011, pp. 1–5. [11] R. V. Koswatta and N. C. Karmakar, “A novel reader architecture based on UWB chirp signal interrogation for multiresonator-based chipless RFID tag reading,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 9, pp. 2925–2933, Sep. 2012. [12] S. Preradovic and N. Karmakar, “Design of fully printable planar chipless RFID transponder with 35-bit data capacity,” in Proc. Microw. Conf., Sep. 29–Oct. 1 2009, pp. 013–016. [13] M. Islam and N. Karmakar, “A novel compact printable dual-polarized chipless RFID system,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 7, pp. 2142–2151, Jul. 2012. [14] S. Hu, C. L. Law, and W. Dou, “A balloon-shaped monopole antenna for passive UWB-RFID tag applications,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 366–368, Jul. 2008. [15] A. Blischak and M. Manteghi, “Embedded singularity chipless RFID tags,” IEEE Trans. Antennas Propag., vol. 59, no. 11, pp. 3961–3968, Nov. 2011. [16] P. Kalansuriya and N. Karmakar, “Time domain analysis of a backscattering frequency signature based chipless RFID tag,” in Asia–Pacific Microw. Conf. Proc., Melbourne, Australia, Dec. 2011, pp. 183–186. [17] P. Kalansuriya and N. Karmakar, “UWB-IR based detection for frequency-spectra based chipless RFID,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [18] C. A. Balanis, Antenna Theory Analysis and Design, 3rd ed. Hoboken, NJ: Wiley, 2005. [19] N. Karmakar, Handbook of Smart Antennas for RFID Systems. Hoboken, NJ: Wiley, 2010 [Online]. Available: http://books. google.com/books?id=WgcSH4G86YAC [20] “Complete technology for 3D EM simulation,” CST Computer Simulation Technology AG, Darmstadt, Germany. [Online]. Available: http:// www.cst.com/ [21] A. Oppenheim, A. Willsky, and S. Nawab, Signals and Systems. Englewood Cliffs, NJ: Prentice-Hall, 1997. [22] R. Bracewell, The Fourier Transform and Its Applications. New York: McGraw-Hill, 2000. [23] E. W. Weisstein, “Rectangle function,” MathWorld—A Wolfram Web Resource. [Online]. Available: http://mathworld.wolfram.com/RectangleFunction.html

Prasanna Kalansuriya (S’08) received the B.Sc. degree (with first-class honors) from the University of Moratuwa, Moratuwa, Sri Lanka, in 2005, and the M.Sc. degree from the University of Alberta, Edmonton, AB, Canada, in 2009. He is currently working toward the Ph.D. degree in electrical and computer systems engineering at Monash University, Clayton, Australia. From 2005 to 2007, he was an Electronic Design Engineer with Electroteks Global Networks, Pte Ltd, Sri Lanka. He has served as a Lecturer with the University of Moratuwa, Moratuwa, Sri Lanka, in 2007, and as a Research Assistant

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with the ICORE Wireless Communication Laboratory, University of Alberta, Edmonton, AB, Canada, from 2008 to 2010. In 2012, he was a Visiting Researcher with the Auto-ID Laboratory, Massachusetts Institute of Technology, Cambridge. His research interests include wireless communication, signal processing for chipless RFID, and applications of chipless RFID and passive RFID in pervasive sensing.

Nemai Chandra Karmakar (S’91–M’91–SM’99) received the M.Sc. degree in electrical engineering from the University of Saskatchewan, Saskatoon, SK, Canada, in 1991, and the Ph.D. degree from the University of Queensland, Brisbane, Australia, in 1999. He is an Associate Professor with the Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Australia. He possesses approximately 20 years of teaching, design, and development experience in antennas, microwave active and passive circuits, and RFIDs in Canada, Australia, and Singapore. He has authored or coauthored over 220 referred journal and conference papers, 24 book chapters, and six books. He has two patents (pending) in chipless RFID technology.

Emanuele Viterbo (M’95–SM’04–F’11) received the Laurea and Ph.D. degrees from the Politecnico di Torino, Torino, Italy, in 1989 and 1995, respectively, both in electrical engineering. From 1990 to 1992, he was with the European Patent Office, The Hague, The Netherlands, as a Patent Examiner working in the field of dynamic recording and error-control coding. Between 1995 and 1997, he held a postdoctoral position with the Dipartimento di Elettronica, Politecnico di Torino, Torino, Italy. During 1997–1998, he was a Post-Doctoral Research Fellow with the Information Sciences Research Center, AT&T Research, Florham Park, NJ. He became first an Assistant Professor (1998) and then an Associate Professor (2005) with the Dipartimento di Elettronica at Politecnico di Torino. In 2006, he became a Full Professor with DEIS, University of Calabria, Italy. Since 2010, he has been a Full Professor with the Department of Electrical and Computer Systems Engineering and Associate Dean for Research Training in the Faculty of Engineering, Monash University, Clayton, Australia. In 1993, he was a Visiting Researcher with the Communications Department, DLR, Oberpfaffenhofen, Germany. In 1994 and 1995, he was visiting the École Nationale Superieure des Telcommunications, Paris, France. In 2003, he was a Visiting Researcher with the Math Department, EPFL, Lausanne, Switzerland. In 2004, he was a Visiting Researcher with the Telecommunications Department, UNICAMP, Campinas, Brazil. In 2005, 2006, and 2009 he was a Visiting Researcher with the ITR, UniSA, Adelaide, Australia. In 2007, he was a Visiting Fellow with the Nokia Research Center, Helsinki, Finland. His main research interests are in lattice codes for the Gaussian and fading channels, algebraic coding theory, algebraic space-time coding, digital terrestrial television broadcasting, and digital magnetic recording. Prof. Emanuele Viterbo is an ISI Highly Cited Researcher and Member of the Board of Governors of the IEEE Information Theory Society (2011–2013). He is an associate editor of the IEEE TRANSACTIONS ON INFORMATION THEORY and Guest Editor for the IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING Special Issue on Managing Complexity in Multiuser MIMO Systems. He Viterbo was awarded a NATO Advanced Fellowship in 1997 from the Italian National Research Council.

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Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers Chao Yu, Student Member, IEEE, Lei Guan, Member, IEEE, Erni Zhu, and Anding Zhu, Member, IEEE

Abstract—The continuously increasing demand for wide bandwidth creates great difficulties in employing digital predistortion (DPD) for radio frequency (RF) power amplifiers (PAs) in future ultra-wideband systems because the existing DPD system requires multiple times the input signal bandwidth in the transmitter and receiver chain, which is sometimes almost impossible to implement in practice. In this paper, we present a novel band-limited digital predistortion technique in which a band-limiting function is inserted into the general Volterra operators in the DPD model to control the signal bandwidth under modeling, which logically transforms the general Volterra series-based model into a band-limited version. This new approach eliminates the system bandwidth constraints of the conventional DPD techniques, and it allows users to arbitrarily choose the bandwidth to be linearized in the PA output according to the system requirement without sacrificing performance, which makes the DPD system design much more flexible and feasible. In order to validate this idea, a high-power LDMOS Doherty PA excited by various wideband signals, including 100-MHz long-term evolution advanced signals, was tested. Experimental results showed that excellent linearization performance can be obtained by employing the proposed approach. Furthermore, this technique can be applied to other linear-in-parameter models. In future ultra-wideband systems, this new technique can significantly improve system performance and reduce DPD implementation cost. Index Terms—Behavioral model, digital predistortion (DPD), linearization, long-term evolution advanced (LTE-advanced), power amplifiers (PAs), Volterra series.

I

I. INTRODUCTION

N order to satisfy growing demands for high data rates and large capacity, transmit signal bandwidth is continuously increasing in modern wireless communication systems. For example, 100-MHz instantaneous modulation bandwidth will be required in the forthcoming long-term evolution advanced (LTE-advanced) systems [1]. This demanding bandwidth requirement creates great difficulties in designing radio frequency (RF) power amplifiers (PAs) to meet efficiency specifications while simultaneously conforming to spectral mask and in-band Manuscript received July 09, 2012; revised September 20, 2012; accepted September 24, 2012. Date of publication November 16, 2012; date of current version December 13, 2012. This work was supported in part by the Science Foundation Ireland under the Principal Investigator Award Scheme and by Huawei Technologies Co. Ltd. This is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17-22, 2012. C. Yu, L. Guan, and A. Zhu are with the School of Electrical, Electronic and Communications Engineering, University College Dublin, Dublin 4, Ireland (e-mail: [email protected]; [email protected]; [email protected]). E. Zhu is with Huawei Technologies Co. Ltd., Shanghai, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222658

distortion requirements. Digital predistortion (DPD) is one of the advanced linearization techniques that compensates for nonlinear distortion in RF PAs by inverting their nonlinear behavior using digital circuits [2]. DPD allows PAs to be operated at higher drive levels for higher efficiency without sacrificing linearity, which is nowadays one of the essential units in high-power wireless base stations [3]. It is well known that the RF PA is inherently nonlinear, and it produces in-band distortion and inter-modulation products that cause spectral regrowth in the adjacent channels. For a modulated signal, fifth-order products appear within a range of five times the bandwidth of the input signal. In order to accurately model and effectively linearize the RF PA, an output signal occupying multiple times the input bandwidth (usually five times) is required to be captured. In the past decades, many DPD models have been developed [4]–[15]. Among them, truncated Volterra series-based models, such as memory polynomial (MP) [5], generalized memory polynomial (GMP) [6], and dynamic deviation reduction-based Volterra series (DDR) [7], are very popular. These models are based on polynomial type of functions of which the output bandwidth increases proportionally with the nonlinear orders. This property can effectively match the nonlinear behavior of the RF PAs, and, hence, these models work very well in the existing systems. However, in the forthcoming wideband system, e.g., LTEadvanced, 100-MHz modulation bandwidth is required, which means that 500-MHz linearization bandwidth will be required if the existing DPD techniques are employed. Such a wide bandwidth requirement will remarkably increase the difficulties in system design. It requires not only very high-speed data converters but also ultra-wideband transmitter and receiver chains, which make DPD sometimes become infeasible. On the other hand, in practice, it may not be necessary to linearize the PA up to such a wideband bandwidth because the signal bandwidth is expanded too wide. We may only need to remove the distortion near the input center frequency band, e.g., within 200-300-MHz range. The distortion beyond that band can be filtered by using a bandpass filter at the PA output, or it may have already been taken care of by the cavity filters in the duplexer. Therefore, in the future system, we may face a scenario that only the distortion within a limited bandwidth is captured, as illustrated in Fig. 1, and we only need to linearize the system within that limited bandwidth. In this new scenario, however, the conventional DPD models can no longer be employed. This is because almost all of the existing models are constructed in the time domain with very little or no control in the frequency domain. For instance, in the MP model, the bandwidth of the frequency-domain signal solely depends on the nonlinear order selected and the distortion resulted from each nonlinear operation are spread

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Fig. 1. Band-limited input and output.

over the corresponding bandwidth. However, in the new system, as shown in Fig. 1, only distortion within a limited bandwidth is captured, and the rest of the distortion is missing, which leads that the signal bandwidth produced by the model does not match the bandwidth of the system under modeling, and thus the model accuracy may be significantly decreased, so that the linearization performance can be deteriorated. In [16], a band-limited Volterra series-based behavioral modeling approach was proposed, which allows us to accurately model a PA with band-limited input and output. This is achieved by inserting a band-limiting function into each Volterra operator before multiplying with its coefficients. By controlling the bandwidth of the band-limiting function, we can arbitrarily choose the bandwidth under modeling. It naturally transforms the general Volterra series-based models into band-limited ones. This approach eliminates the inherent bandwidth requirement of the general Volterra series but still keeps the same model structure, such as the linear-in-parameter property. Experimental results showed that the proposed approach significantly improves the model accuracy. In this paper, we introduce a band-limited DPD system by employing the proposed modeling technique. In this new system, the DPD bandwidth can be arbitrarily chosen according to the system requirement, which removes the system bandwidth constrains of the conventional system. It provides an extra freedom for DPD designers to make tradeoffs between linearization bandwidth and system cost. Detailed theoretical analysis and rigorous experimental validations are presented in the paper. This paper is organized as follows. In Section II, we briefly reintroduce the band-limited behavioral modeling methodology proposed in [16]. A band-limited DPD system is then proposed in Section III while the model implementation is presented in Section IV. Experimental results are given in Section V with a conclusion in Section VI. II. BAND-LIMITED BEHAVIORAL MODELING A. General Volterra Series In the discrete time domain, a general Volterra series [17] can be written as (1)

Fig. 2. General Volterra series model.

where tively,

and

represent the input and output, respecis the th-order Volterra kernel, and (2)

is the th-order Volterra operator. In a real applicawhere tion, the general Volterra series is normally simplified to a certain format. For instance, only limited dynamic orders are considered in the DDR-Volterra model [7]. One of the main advantages of the Volterra models is that the output of the model is linear with respect to its coefficients, meaning that it is possible to extract a nonlinear Volterra model in a direct way by using linear system identification algorithms, such as least squares (LS). However, one common feature of these models is that the signal bandwidth in the frequency domain increases with the nonlinear orders involved in the model. As shown in Fig. 2, when the input signal passes each nonlinear Volterra operator, the signal bandwidth proportionally increases with the order of nonlinearity selected. For example, the third-order operator will expand the signal bandwidth three times, and the final output bandwidth depends on the highest order of nonlinearity chosen. Sufficient accuracy can be achieved when the nonlinear order in the model matches the bandwidth of the system under modeling. For instance, a fifth-order model can be used when the output signal within five times the input signal bandwidth is captured. However, in the wideband scenario described earlier, the output signal may be filtered before it is captured. In that case, although

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Fig. 3. Band-limited Volterra series model.

the high-order nonlinear distortion is spread over a wide bandwidth, only part of distortion within the filter passband is obtained while the other part is missing. If we still use the Volterra model to map the input to the output, the model accuracy will decrease because the signal bandwidth of the model does not match the signal bandwidth under modeling. B. Proposed Band-Limited Volterra Series To resolve the bandwidth mismatch problem, a new model called band-limited Volterra series was proposed [16], in which a band-limiting function is introduced to control the bandwidth expansion when the signal passes each nonlinear Volterra operis inator. As shown in Fig. 3, a band-limiting function serted into the Volterra operator. This band-limiting function can be a linear filter, and it can be predesigned in the frequency domain with an effective bandwidth chosen according to the bandwidth requirement of the system output. It is then converted into the time domain and represented by a finite impulse response. The new th-order band-limited Volterra operator can be represented by (3) represents the convolution operation. The general where Volterra series can thus be transformed into a band-limited version as

it passes each Volterra operator, the bandwidth of the output from each Volterra operator is limited within a certain frequency range, e.g., BW. After linearly scaled by the coefficients and reis logically band-limcombined together, the final output ited to BW. It allows the bandwidth of the signal produced by the model to perfectly match that of the actual PA output if BW is chosen to be equal to the bandwidth of the PA output. The accuracy of the model is therefore significantly increased. Although linear convolution is required, the model structure is still the same as that of the general Volterra series, e.g., the output is still linear with respect to the model parameters. The coefficients can therefore also be extracted by using linear system identification algorithms. By inserting a band-limiting function into each Volterra operator, the general Volterra series is naturally transformed into the band-limited version. This intervention to the model completely changes the model behavior and significantly enhances its modeling capability. In the conventional model, there is no control in the frequency domain and the bandwidth of the output is solely decided by the nonlinear order chosen. In the new model, an extra control or freedom is obtained, namely, we can arbitrarily control the signal bandwidth produced by the model in the frequency domain by selecting different bandwidths of the band-limiting function, despite the model is still operated in the time domain. In this case, no matter how narrow the bandwidth of the PA output is, the relationship between the input and output can always be accurately represented by the new model if the bandwidth of the band-limiting function matches that of the PA output. If we consider integrating the band-limiting function with the original Volterra operator together, we can treat the as a new basis new nonlinear operation function. The model based on the new band-limited basis function can be used to represent a wide range of nonlinear systems, including the general Volterra series if the filter bandwidth is set to infinite. In this sense, the general Volterra series can be treated as one of special cases of the new model. III. BAND-LIMITED DIGITAL PREDISTORTION The band-limited modeling idea proposed in Section II looks very simple. However, it not only just improves the model accuracy, but also significantly enhances the modeling capability. If employed in DPD, it dramatically changes the way the DPD system is operated, as we will discuss below. A. Conventional DPD

(4) is the th-order band-limited Volterra operator, where is the band-limiting function with length , is the th-order band-limited Volterra kernel, and and represent the input and output, respectively. As shown in Fig. 3, because the signal is filtered by the band-limiting function after

In the conventional systems, behavioral models developed for RF PAs can be directly employed in DPD and the indirect learning approach [18], [19] is normally used for model extraction. It is based on the theory of the th-order inverse described in the classical Volterra series book [17], which states that the th-order post-inverse is the same as its th-order pre-inverse when a nonlinear system is linearized up to the th-order nonlinearity. In these systems, an identical model is normally used for both the pre-inverse in predistortion and the post-inverse in model extraction. In the model extraction, the output of the PA is used as input of the model while the input of the PA is used as the expected output. The extracted coefficients

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Fig. 4. Cascaded nonlinear system. Fig. 6. Band-limited cascaded nonlinear system.

Fig. 5. Conventional DPD.

are then directly copied to the pre-inverse model, i.e., the predisapproaches , tortion block, as illustrated in Fig. 4. If is then close to . As mentioned earlier, a signal passing a nonlinear PA will generate spectrum regrowth, and the nonlinear operators in the DPD model also expand the signal bandwidth. In the frequency domain, we can see the signal bandwidth changes when the signal passes each nonlinear block, as illustrated in Fig. 4: 1) in the post-inverse case, when the original input signal passes the PA, the bandwidth of the signal is expanded five times, and then after the post-inverse, the signal bandwidth returns to the original bandwidth and 2) in the pre-inverse case, the signal bandwidth is expanded five times when the signal passes the predistorter block and then returns to the original after passing the PA. In a real system, DPD is normally operated in digital baseband. The block diagram of a general DPD system is shown in Fig. 5. In order to accommodate the frequency-domain characteristics and achieve high linearization performance, a general rule of thumb is that five times the input signal bandwidth would be required in both the feedback path and the transmitter chain. The configuration in Fig. 5 works very well in a relatively narrowband system. However, for a wideband system, e.g., the LTE-Advanced system, 100-MHz input bandwidth will be required. If the existing DPD system is used, 500-MHz linearization bandwidth will be needed. It creates enormous difficulties in real implementation. In the feedback path, a wideband down-conversion chain is required and a 500-Mega-samples-per-second (MSPS) sampling rate will be required for the analog-to-digital converters (ADCs) for I/Q

signals.1 If digital intermediate frequency (IF) signal is used, it will require 1-Giga-samples-per-second (GSPS) sampling. In order to produce the 500-MHz predistorted signal and allow it to pass through the transmitter chain before feeding into the PA, very high-speed digital-to-analog converters (DACs) and a wideband transmitter chain will also be required. This is very difficult and sometimes impossible to implement in practice. On the other hand, it may not be necessary to clean up all of the distortions in such a wide bandwidth by using DPD because, when the distortion is spread into such a wide bandwidth, some distortions in the sideband can be easily filtered by using a bandpass filter in the output of the RF PA, and this bandpass filter may have already existed in the transmitter, e.g., the cavity filter in the duplexer. Therefore, in practice, it would be desirable to have a DPD system that only requires limited bandwidth and only linearizes the PA up to a certain bandwidth. However, this will require necessary changes in the existing DPD models; otherwise, the system performance will deteriorate quickly. This is because the model accuracy is significantly reduced when the bandwidth of the system under modeling does not match the signal bandwidth of the model, as discussed in Section II. B. Proposed Band-Limited DPD If the band-limited model proposed in Section II is employed, the bandwidth mismatch problem can be easily resolved. Assuming that the output of the PA is filtered, the system under modeling can be represented by a nonlinear PA with a bandpass filter, as represented by shown in Fig. 6. If we let the bandwidth of the band-limiting function be equal to the bandwidth of the bandpass filter, the relationship between the PA input and output can be accurately modeled by employing the band-limited model. Because part of the frequency information is missing, invertibility of the model must be investigated before employing it in DPD. First, let us look at how the signal is handled by the model. In the PA modeling (the forward model), because we changed the basis function of the model, the frequency bandwidth of the model can now perfectly match the bandwidth of the system under modeling. With correct model extraction, the input and output relationship can be accurately represented 1The ADC sampling rate may be reduced by employing the under-sampling approach proposed in [8], but the anti-aliasing filter in the ADC must be redesigned to preserve the full sideband information, and it still requires a wideband down-conversion chain in the feedback path.

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by a th-order band-limited Volterra model. Despite the fact that each of the new Volterra operator only takes into account the information within the selected bandwidth, there must be one-to-one mapping from the input to the output in the transfer function, which is the same as that in the general Volterra series. For instance, the third-order basis function exactly represents the mapping from the original input to the band-limited third-order distortion. Therefore, in an inverse order, if the same band-limited model structure is used and with the same signal bandwidth, the one-to-one mapping can of course be inverted back in the same way. Hence, the model indeed is invertible. Second, we should discuss whether or not the th-order inverse is still applicable. Let us rederive the equations in the th-order inverse theory [17]. As illustrated in Fig. 6, we simply cascade the three systems together, similar to that in Fig. 4. We with a bandfirst construct a th-order post-inverse . limited model, and then copy it into the pre-inverse, Let us assume (5) in the system

Fig. 7. Band-limited DPD.

Using (13), we obtain (15) and, using (10), we obtain (16)

with the post-inverse (6)

is the th-order band-limited Volterra operator with where the post-inverse and in the pre-inverse

Comparing (15) with (16), we obtain (17) and thus (18)

(7) Following the same procedure, we can obtain

so that

(19)

(8) Because the bandwidths of all three nonlinear systems are limited within the selected bandwidth, the overall system can also be represented by a band-limited Volterra model as (9) where is the th-order band-limited Volterra operator. From (8) and (9), we can obtain (10) Let us look at the first-order term, (11) and, in the mean time, in the post-inverse, we have (12) and represent the first-order term of and where , respectively. Comparing (11) with (12), we can obtain (13) For the second-order term, in the post-inverse, we have (14)

Finally, we can obtain (20) where is the th-order band-limited Volterra operator of the approaches system with the pre-inverse. It shows that, if , is also close to within the th-order nonlinearity, which means that the th-order inverse is still applicable in this band-limited system. Because there is no explicit designation of bandwidth constraints in the above derivation, we can also conclude that the selected DPD bandwidth does not affect the linearization performance as long as the bandwidth of the DPD matches that of the PA output. In other words, no matter how narrow the linearization bandwidth is, the distortion within the selected bandwidth will always be reduced to the same level. The minimum bandwidth of the DPD would be the input signal bandwidth. Based on the analysis above, a new DPD system can be constructed as shown in Fig. 7. Compared with the conventional system in Fig. 5, only two changes need to be made: 1) a bandpass filter is used in the PA output and 2) a band-limiting function is inserted into the DPD model to control the linearization bandwidth that must match the bandwidth of the bandpass filter at the PA output. In this new system, the DPD bandwidth can

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be arbitrarily chosen according to the system requirement. For instance, if we only want to linearize up to 200 MHz for the 100-MHz input signal illustrated in Fig. 7, we can simply set the bandpass filter bandwidth to 200 MHz and filter out the out of band distortion before capture the 200 MHz signal in the observation path. In the transmitter chain, only 200 MHz predistorted signal is transmitted. The sampling rate of the data converters is thus reduced to 200 MSPS for I/Q signals and 400 MSPS for digital IF. Although there are still distortions in the PA output beyond 200 MHz after digital predistortion, these distortions can be filtered by the bandpass filter, and the original signal is restored in the final output. In summary, the new band-limited modeling methodology provides an additional freedom for users to choose the bandwidth to be linearized when designing a DPD system, which eliminates the system bandwidth constraints. It can significantly improve the system performance and reduce the cost of the overall system. IV. DPD IMPLEMENTATION After introducing the general structure of the band-limited DPD, we now move to model construction and parameter extraction.

where and represents the complex envelopes of the input and output, respectively, is the complex Volterra kernel of the system, is the order of nonlinearity and is an odd number, and is the memory length. In the band-limited system, a complex baseband low-pass filter can be used as the band-limiting function and inserted into the basis function of the original model, which can be conducted by using linear convolution. The new band-limited model can therefore be written as given by (22), shown at the bottom of the page, where is the baseband band-limiting function with length , is the band-limited complex Volterra kernel of the system. In matrix form, the new model can be represented as (23) where is the number of data samples and is the number of coefficients, is the coefficients matrix containing all coefficients, (24)

A. Model Construction The proposed band-limited modeling approach can be applied to any linear-in-parameter models. In this work, we use the simplified second-order DDR-Volterra model [20] as an example. The original DPD function is written as

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and

is the output matrix generated from the predistorted input as (25)

(21)

is the input matrix generated from the original input , containing all linear and nonlinear terms appearing in the input of the model represented by (22), which can be formed as given by (26), shown at the bottom of the following page. As described in [21], a single-function-based DPD may not be sufficient to linearize some types of RF PAs, e.g., envelope tracking or multistage Doherty amplifiers. The vector decomposition technique [21] can then be used to form a decomposed piecewise Volterra model to characterize a wider range of nonlinear systems. In the band-limited case, this technique can also be directly applied.

(22)

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sampling rate of data converters. To vary the system bandwidth, we processed the signal in the digital domain to emulate the bandwidth changes in the analog domain instead. For instance, in the 80-MHz case, we filtered the 140-MHz signal captured from the bench to 80 MHz in the digital domain before conducting the model extraction and DPD. The performance should match that of the physical changes in a real system, although other factors may need to be considered, e.g., noise floor of the ADCs and filters. However, for verifying the idea proposed in this paper, it does not make much difference. A. Proposed Model Versus Conventional Model

Fig. 8. Experimental test bench setup.

B. Model Parameter Extraction To extract the coefficients, the indirect learning [18], [19] can be employed, where the feedback signal, i.e., the output of the PA is used as the input of the model, while the predistorted input signal is used as the expected output. By employing the standard LS algorithm, the coefficients vector can be estimated from (27) is conwhere is the extracted coefficients with length , structed from the PA output in the same way of , and is the expected inverse output matrix generated from the PA input (the output of the predistorter), . In the first iteration, is equal to . V. EXPERIMENTAL RESULTS Here, the performance of band-limited Volterra DPD will be validated in several experimental tests. A high-power LDMOS Doherty PA operated at 2.14 GHz was used. The test bench was set up as shown in Fig. 8. A baseband I/Q complex signal source is generated in MATLAB from the PC and sent into the baseband board. The baseband signal is first converted into the analog domain and then modulated and up-converted to the RF frequency. The signal then passes a driver and is finally fed into the main PA. In the feedback loop, the output of the PA is down-converted to baseband and captured back to the PC. The baseband I/Q data sampling rate is 184.32 MSPS, and the system bandwidth is limited to 140 MHz. Due to hardware limitations, we could not arbitrarily change the analog filter bandwidth on the PA output or the

.. .

.. .

In order to validate the linearization performance, we first compared the proposed DPD model with the conventional DPD model. The test was conducted in three scenarios: 1) the conventional model with a sufficient bandwidth; 2) the conventional model with a limited bandwidth; and 3) the proposed model with a limited bandwidth. A 20-MHz four-carrier WCDMA signal with peak-to-average power ratio (PAPR) of 6.5 dB was used to excite the PA with an average output power at 36 dBm. In the sufficient bandwidth scenario, the system bandwidth was set to 140 MHz, which was seven times the input signal bandwidth. Therefore, almost all of the distortions caused by the PA nonlinearities and memory effects were captured. In the band-limited scenarios, the system bandwidth was set to only two times the input bandwidth, i.e., 40 MHz. The DPD model employed was the decomposed piecewise second-order DDR model discussed in Section IV. The magnitude threshold was set as 0.5 for the normalized data, the corresponding nonlinearity order was se, and the memory length was set to . In lected as theory, the band-limiting function in the proposed model should be an ideal rectangular filter, but, in practice, it can be a normal FIR filter, and the order and the type of the filter can be chosen according to the real system performance requirement. In this test, an equiripple low-pass filter was chosen, and its bandwidth was set to 40 MHz. To eliminate the effects induced by the filter, we used a very high-order filter with 266 coefficients in the initial test, but the order of the filter was reduced in the late test for other performance evaluations. The test results are shown in Table I, and the frequencydomain spectra are plotted in Fig. 9. We can see that the conventional model can achieve excellent performance when a sufficient linearization bandwidth is provided. 30-dB adjacent channel power ratio (ACPR) reduction can be obtained and normalized mean square errors (NMSE) is reduced from 21

.. .

.. .

(26)

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TABLE I PERFORMANCE FOR 20-MHZ 4-CARRIER WCDMA SIGNAL

Fig. 9. Output spectra in comparison between the proposed model and the conventional model.

Fig. 10. AM/AM and AM/PM characteristics with/without proposed DPD for a four-carrier 20-MHz WCDMA signal with 40-MHz linearization bandwidth.

to 46 dB. However, when the system bandwidth is reduced, the performance of the conventional model is dramatically deteriorated (9 and 15 dB worse in ACPR with 5- and 10-MHz frequency offset, respectively), when the DPD bandwidth is reduced from 140 to 40 MHz. However, if the proposed DPD is employed, almost the same performance can be achieved as that of the conventional model within the selected linearization

Fig. 11. Output spectra under different linearization bandwidths: (a) 140 MHz, (b) 120 MHz, (c) 100 MHz, and (d) 80 MHz.

bandwidth. After filtering, the original signal can be restored. Fig. 10 shows the AM/AM and AM/PM characteristics before

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Fig. 12. NMSE and ACPR values versus different linearization bandwidths.

and after the proposed DPD, where we can see that the distortion caused by the PA nonlinearities and memory effects can be effectively removed. B. Performance With Various Linearization Bandwidths In Section V-A, we compared the performance produced by the proposed model with that by the conventional model within a fixed bandwidth. Here, we verify how the system bandwidth changes affect the linearization performance. In this test, a 60-MHz 12-carrier UMTS signal with PAPR of 6.5 dB was used to excite the PA and again with an average output power at 36 dBm. The same model was used as that in Section A, except the memory length was set to . The system bandwidth was varied from 140 to 80 MHz. The bandwidth of the band-limiting function was set to the correspondent system bandwidth, and the order of the filter was reduced to 82. The spectra of the PA output with and without DPD are plotted in Fig. 11, where we can see that the linearization performance is kept almost the same, with 29-dB improvement in ACPR, within the selected bandwidth from 140 to 80 MHz. It can be further verified by calculating the NMSE and ACPR values under the different system bandwidths. As presented in Fig. 12, both NMSE and ACPR values only fluctuated within a very small range. This test result confirms that the system bandwidth changes do not affect the linearization performance as long as the DPD model bandwidth matches the system under modeling, which also verifies the conclusion made in Section III-B. C. Performance With Various Signal Configurations Here, we employ the proposed DPD model to linearize a system excited with further wider band signals and with different signal configurations, e.g., 100-MHz signals in three scenarios: 1) five-carrier LTE-Advanced signal with contiguous configuration and with a PAPR of 7.8 dB; 2) three-carrier LTEAdvanced signal with noncontiguous configuration and with a PAPR of 7.7 dB; and 3) LTE-Advanced UMTS mixed-mode signal with a PAPR of 9.2 dB. The configurations for the DPD model were the same as that in Section V-B, except that the bandwidth is fixed at 140 MHz. Fig. 13 shows the frequency-domain spectra in three scenarios, and the NMSE and ACPR values are listed in Table II. From these results, we can see that the conventional model did not

Fig. 13. Output spectra under different scenarios. (a) Scenario 1. (b) Scenario 2. (c) Scenario 3.

perform well, while the proposed model consistently achieved excellent performance. From the spectra, we can clearly see that not only was the out-of-band distortion reduced but also the in-band distortion was cleaned up. This again verifies the conclusion made earlier. To the best of the authors’ knowledge, this is the first high-performance linearization result for 100-MHz signals published to date.

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TABLE II PERFORMANCE FOR 100-MHZ SIGNALS

VI. CONCLUSION In this paper, a novel band-limited Volterra series-based behavioral model and its related DPD system have been presented. Theoretical analysis and experimental results showed that this new band-limited modeling technique not only significantly improves the model accuracy but, more importantly, eliminates the system bandwidth constraints of the conventional DPD techniques. It provides an extra freedom for DPD designers to arbitrarily choose the bandwidth to be linearized in the PA output according to the system requirement without sacrificing performance, which makes the system design much more flexible and practical. Furthermore, this modeling technique is very general. It is not limited to the Volterra series-based models that we presented in this paper, but it also can be applied to other linear-in-parameters models. In future ultra-wideband systems, this new technique can significantly improve system performance and reduce DPD implementation cost. We expect that this technique will have a significant impact on the DPD field. REFERENCES [1] T. Ali-Yahiya, Understanding LTE and its Performance. New York: Springer, 2011. [2] P. B. Kennington, High Linearity RF Amplifier Design. Norwood, MA: Artech House, 2000. [3] F. Luo, Digital Front-End in Wireless Communications and Broadcasting. Cambridge, U.K.: Cambridge Univ., 2011. [4] F. M. Ghannouchi and O. Hammi, “Behavioral modeling and predistortion,” IEEE Microw. Mag., vol. 10, no. 7, pp. 52–64, Dec. 2009. [5] J. Kim and K. Konstantinou, “Digital predistortion of wideband signals based on power amplifier model with memory,” Electron. Lett., vol. 37, no. 23, pp. 1417–1418, Nov. 2001. [6] D. R. Morgan, Z. Ma, J. Kim, M. G. Zierdt, and J. Pastalan, “A generalized memory polynomial model for digital predistortion of RF power amplifiers,” IEEE Trans. Signal Process., vol. 54, no. 10, pp. 3852–3860, Oct. 2006. [7] A. Zhu, J. C. Pedro, and T. J. Brazil, “Dynamic deviation reduction based Volterra behavioral modeling of RF power amplifiers,” IEEE Trans. Microw Theory Tech., vol. 54, no. 12, pp. 4323–4332, Dec. 2006.

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[8] A. Zhu, P. J. Draxler, J. J. Yan, T. J. Brazil, D. F. Kinball, and P. M. Asbeck, “Open-loop digital predistorter for RF power amplifiers using dynamic deviation reduction-based Volterra series,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 7, pp. 1524–1534, Jul. 2008. [9] S. Hong, Y. Y. Woo, J. Kim, J. Cha, I. Kim, J. Moon, J. Yi, and B. Kim, “Weighted polynomial digital predistortion for low memory effect Doherty power amplifier,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 5, pp. 925–931, May 2007. [10] T. Liu, S. Boumaiza, and F. M. Ghannouchi, “Augmented Hammerstein predistorter for linearization of broadband wireless transmitters,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 1340–1349, Jun. 2006. [11] J. Kim, Y. Y. Woo, J. Moon, and B. Kim, “A new wideband adaptive digital predistortion technique employing feedback linearization,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 2, pp. 385–392, Feb. 2008. [12] N. Safari, T. Røste, P. Fedorenko, and J. S. Kenny, “An approximation of Volterra series using delay envelopes, applied to digital predistortion of RF power amplifiers with memory effects,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 2, pp. 115–117, Feb. 2008. [13] O. Hammi, S. Carichner, B. Vassilakis, and F. M. Ghannouchi, “Synergetic crest factor reduction and baseband digital predistortion for adaptive 3G Doherty power amplifier linearizer Design,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 11, pp. 2602–2608, Nov. 2008. [14] S. A. Bassam, W. Chen, M. Helaoui, F. M. Ghannouchi, and Z. Feng, “Linearization of concurrent dual-band power amplifier based on 2D-DPD technique,” IEEE Microw. Wireless Compon. Lett., vol. 21, no. 12, pp. 685–687, Dec. 2011. [15] H. Cao, H. M. Nemati, A. S. Tehrani, T. Eriksson, and C. Fager, “Digital predistortion for high efficiency power amplifier architectures using a dual-input modeling approach,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 2, pp. 361–369, Feb. 2012. [16] C. Yu, L. Guan, and A. Zhu, “Band-limited Volterra series-based behavioral modeling of RF power amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [17] M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems. Melbourne, FL: Krieger, 1989. [18] C. Eun and E. J. Powers, “A new Volterra predistorter based on the indirect learning architecture,” IEEE Trans. Signal Process., vol. 45, no. 1, pp. 223–227, Jan. 1997. [19] L. Ding, G. T. Zhou, D. R. Morgan, Z. Ma, J. S. Kenney, J. Kim, and C. R. Giardina, “A robust digital baseband predistorter constructed using memory polynomials,” IEEE Trans. Commun., vol. 52, no. 1, pp. 159–165, Jan. 2004. [20] L. Guan and A. Zhu, “Simplified dynamic deviation reduction-based Volterra model for Doherty power amplifiers,” in Proc. IEEE Int. Integr. Nonlinear Microw. Millimeter-Wave Circuits Workshop, Vienna, Austria, Apr. 2011, pp. 1–4. [21] A. Zhu, P. J. Draxler, H. Chin, T. J. Brazil, D. F. Kimball, and P. M. Asbeck, “Digital predistortion for envelope-tracking power amplifiers using decomposed piecewise Volterra series,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 10, pp. 2237–2247, Oct. 2008.

Chao Yu (S’09) received the B.E. and M.E. degrees from Southeast University, Nanjing, China, in 2007 and 2010, respectively. He is currently working toward the Ph.D. degree at University College Dublin, Dublin, Ireland. His research interests include antenna design, behavioral modeling, and digital predistortion for RF power amplifiers.

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Lei Guan (S’09–M’12) received the B.E. and M.E. degrees from Harbin Institute of Technology, Harbin, China, in 2006 and 2008, respectively, and the Ph.D. degree from University College Dublin, Dublin, Ireland, in 2012, all in electronic engineering. He is currently a Senior Research Engineer with the School of Electrical, Electronic and Communications Engineering, University College Dublin, Dublin, Ireland. His research interests include linearization and system-level modeling of RF/microwave power amplifiers with emphasis on digital predistortion-based PA linearization and its FPGA hardware implementation. He also has interests in nonlinear system identification algorithms, digital signal processing, wireless communication system design, and FPGA-based parallel computing.

Erni Zhu, photograph and biography not available at the time of publication.

Anding Zhu (S’00–M’04) received the B.E. degree in telecommunication engineering from NorthChina ElectricPower University, Baoding, China, in 1997, the M.E. degree in computer applications from Beijing University of Posts and Telecommunications, Beijing, China, in 2000, and the Ph.D. degree in electronic engineering from University College Dublin, Dublin, Ireland, in 2004. He is currently a Lecturer with the School of Electrical, Electronic and Communications Engineering, University College Dublin, Dublin, Ireland. His research interests include high-frequency nonlinear system modeling and device characterization techniques with a particular emphasis on Volterra-series-based behavioral modeling and linearization for RF PAs. He is also interested in wireless and RF system design, digital signal processing, and nonlinear system identification algorithms.

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Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin Volker Ziegler, Senior Member, IEEE, Benedikt Schulte, Jordi Sabater, Sergio Bovelli, Juergen Kunisch, Kai Maulwurf, Marta Martinez-Vazquez, Senior Member, IEEE, Christos Oikonomopoulos-Zachos, Member, IEEE, Srdjan Glisic, Marcus Ehrig, and Eckhard Grass

Abstract—This paper describes the specific development of a high-data-rate 57–64-GHz point-to-multipoint wireless local-area network communication system and the worldwide first installation of such a system into an aircraft cabin mock-up. All of the system components, from the RF-chip-set, the low-temperature cofired ceramic integrated antennas, and RF modules to the baseband processor, the medium access control, and the application software were purpose-designed for a wireless backbone for in-cabin communication. The integration aspects of these system components into a passenger aircraft cabin mock-up (ceiling and passenger seat-integration) as well as successful system performance tests were carried out and are reported here. Index Terms—Communication systems, microwave antennas, microwave integrated circuits, wireless local-area network (WLAN).

cies for mobile devices. Therefore, a high-data-rate 57–64-GHz point-to-multipoint system for in-cabin communication (crew and passengers) was specifically developed [3]. It combines the advantages of: 1) low electromagnetic interference, which leads to easier certification; 2) reduced installation and configuration efforts for crew and maintenance staff; and 3) higher flexibility of cabin seat arrangements and reconfiguration during the turn-around time or in the initial configuration setup. The paper presents all system components like the RF chipset, the low-temperature cofired ceramic (LTCC)-integrated antennas, the RF modules, the medium-access control, the baseband processor, and the application software as well as their cabin integration and final system performance tests in the aircraft cabin mock-up.

I. INTRODUCTION

II. FREQUENCY REGULATION AND STANDARDIZATION

IRLINES request more flexibility and more built-in support for changes in the cabin layout, in particular, not being restricted by the current electrical installation of cabin-management and in-flight-entertainment systems connected by wires to each and every seat [1]. Consequently, the objective of the development was to have passenger seats with wireless data and power connections. Regarding the wireless data connections, existing commercial wireless local-area network (WLAN) technologies in the lower ISM bands (2.4–2.5 GHz and 5.725–5.875 GHz) are often not sufficient in terms of data throughput and user density to realize the vision of a wireless cabin backbone. The first implementations of WiFi-based in-flight entertainment systems are currently being piloted [2], but the targeted application requires higher system security and, consequently, does not use the common frequen-

Depending on the country, there is about 7 GHz of bandwidth license-free as an ISM band available worldwide. This is significantly more than all other ISM bands together. The transmit power allowed for indoor applications is approximately 10 dBm, corresponding to 40 dBm of equivalent isotropically radiated power (EIRP). This very liberal frequency regulation facilitates the development and application of short-range, high-data-rate communication systems operating over a distance of 20 m and with data rates of well beyond 1 Gb/s. [4]. To harmonize the use of this huge amount of bandwidth, several international standards, specifying high-data-rate wireless communication systems, were developed. A comparison of some main parameters is provided in Table I. After the first standard, ECMA 387 [5], was released in 2008, the Wireless PAN standard IEEE 802.15.3c was completed in 2009 [6]. A new wireless LAN standard IEEE802.11ad is in the final specification before being released in mid-2012 [7]. Common to all three standards is the channel plan. Four frequency channels, each having a bandwidth of 2.16 GHz, are specified. In addition to these four channels, the ECMA 387 standard supports channel bonding of two, three, and four adjacent channels. Another feature common to all three standards is the support of beamforming. In our opinion, due to the strong industrial support (WiGig consortium), the new WLAN standard IEEE802.11ad has the highest potential for widespread adoption in future industrial and consumer application. All three standards use orthogonal frequency-division multiplexing (OFDM), in particular for the high data-rate modulation and coding schemes. With OFDM, a high degree of ro-

A

Manuscript received July 05, 2012; revised September 14, 2012; accepted September 27, 2012. Date of publication November 29, 2012; date of current version December 13, 2012. This work was supported by the German Federal Ministry of Education and Research under Contract EASY-A 01BU0804. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. V. Ziegler and S. Bovelli are with EADS Innovation Works, 81663 Ottobrunn, Germany (e-mail: [email protected]). B. Schulte was with EADS Innovation Works, 81663 Ottobrunn, Germany. He is now with Astyx GmbH, 85521 Ottobrunn, Germany. J. Sabater is with AED Engineering GmbH, 81663 Munich, Germany. J. Kunisch, K. Maulwurf, M. Martinez-Vazquez, and C. OikonomopoulosZachos are with IMST GmbH, 47575 Kamp-Lintfort, Germany. S. Glisic, M. Ehrig, and E. Grass are with IHP GmbH, 65929 Frankfurt (Oder), Germany. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222914

0018-9480/$31.00 © 2012 IEEE

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TABLE I COMPARISON OF 60-GHZ STANDARDS

Fig. 1. WLAN in-cabin communication system: system architecture.

bustness against the effects of multipath propagation—faced in an aircraft cabin—is achieved and consequently chosen for the system demonstrator. Even though the developed demonstrator is not fully standard compliant, our findings are applicable to future systems adhering to one of the 60-GHz standards—in particular to the IEEE802.11ad WLAN standard.

Fig. 2. Transmitter architecture of the 57–64-GHz front-end.

III. SYSTEM ARCHITECTURE AND DEMONSTRATOR The complete WLAN communication system consists of several access points hidden in the cabin ceiling above the aisles and user terminals, which are integrated into the passenger seats. Each access point is able to deliver a data rate of 1 Gb/s to several rows of seats. In order to find the optimum number and positions of access points and seat terminals, ray-tracing simulations [8] of the complete aircraft cabin were performed taking into account: • line-of-sight blocking by sitting and moving people; • link budget; • high quality of service (QoS); • smallest number of access points with maximum coverage. From the results of these analyses, it was concluded that the optimum configuration is one access point supplying six rows of seats, while each row of seats has one link to two access points each for a high QoS. Between the two links, there will be a seamless handover in case of line-of-sight blockage by passengers or crew members. In order to demonstrate the feasibility and performance of this approach, a complete system demonstrator was developed. It consists of two access points (APs) installed in the ceiling of the aircraft cabin and a row of passenger seats equipped with two seat-terminal transceivers (STT) to demonstrate the seamless handover between two access points. The principle system architecture of the access points and the STTs is illustrated in Fig. 1. Both the AP and the STT are

based on a LTCC board for the RF front-end and antennas, a field-programmable gate array (FPGA) board for the baseband processing and medium-access control (MAC) layer and a Linux board for the application software and the adaptation layer driver. On the AP side, the system in connected to a video server by a Gigabit Ethernet cable, and the same connection is used on the STT side to the touch screen. Since the RF signal has to pass through different cabin materials, an in-depth investigation of the transmission losses of various materials (e.g., foam of the seat, several seat covers, ceiling, and sidewall panels) was performed at 57–64 GHz and used for the channel modeling and link-budget calculations. The highest transmission losses measured for typical cabin materials were around 3 dB, which were taken into account during initial link-budget calculations. IV. 57–64-GHZ RF FRONT-ENDS A. Highly Integrated SiGe BiCMOS RF Chipset A fully integrated transmitter (Tx) and receiver (Rx) front-end chipset was specifically designed for the system demonstrator with a modified heterodyne topology with a sliding intermediate frequency. The chipset was fabricated in a 0.25- m SiGe:C BiCMOS technology [9]. The architecture of the transmitter with the Tx front-end block diagram is shown in Fig. 2. It consists of a 12-GHz I/Q

ZIEGLER et al.: BROADBAND 57–64-GHZ WLAN COMMUNICATION SYSTEM INTEGRATED INTO AN AIRCRAFT CABIN

mixer, an intermediate frequency (IF) amplifier, a phase-locked loop (PLL), a 60-GHz mixer, an image-rejection filter, and a power amplifier (PA). Differential I and Q input signals are fed into a quadrature mixer. The mixer itself consists of linearized double-balanced Gilbert cells and is followed by an IF buffer amplifier. The input signals are up-converted with a quadrature 12-GHz signal from the PLL. The quadrature mixer biasing can be controlled with a monolithically integrated Serial Peripheral Interface (SPI). The dc currents of the two branches of each double-balanced mixer can be controlled separately. This allows optimization of sideband suppression and conversion gain. A double-balanced Gilbert cell is used as up-conversion mixer core for the second up-conversion. The IF signal is up-converted in the mixer with the 48-GHz oscillator signal from the integrated PLL. The result is a double-sideband spectrum with a signal at 60 GHz and an out-of-band image at 36 GHz. The PLL is a critical component for the performance of the whole system, because OFDM signals are sensitive to the phase noise of the PLL signal. The spur level is not critical, but it should be below 45 dBc to keep the integrated phase error small. The measured PLL phase noise at 48 GHz is 98 dBc/Hz at 1-MHz offset. This phase noise is rather high for 64 quadrature-amplitude modulation (QAM), but is suitable for 16-QAM transmission. The measured PLL bandwidth is 150 kHz, and the tuning range is from 47.2 to 49.6 GHz. The purpose of the filter is to attenuate both the image at 36 GHz and the VCO feed-through at 48 GHz. A strong feedthrough signal would affect the linearity of the receiver frontend, because the transmitter and receiver antennas are placed in close proximity. The -factor of integrated inductors for the 60-GHz range is low (typically 15 to 20), resulting in high insertion loss and limited selectivity. For a compact design, a lumped-element filter type was chosen. The measured insertion loss is 3.3 dB at 60 GHz. The image rejection at 36 GHz is 27.7 dB. The VCO feed-through at 48 GHz is attenuated by 12 dB. The PA features a three-stage differential cascode topology. This offers a high gain of around 11 dB per stage in Leibniz Institut Innovations for High Performance Microelectronics (IHP) technology and good matching at both input and output. The PA, like the rest of the chip, is fully differential for doubling the output power, which is combined with a differential antenna. The complete Tx-chain and especially the PA require good on-chip ground for stable operation. In order to achieve this, the ground connection needs many short bondwires. In addition, the PA layout is drawn symmetrically utilizing the virtual ac ground for the differential signal at the symmetry line of the layout. The matching topology between stages is an LC structure. The inductances were realized as lines in the top metal layer. They were bent in the layout in order to end at the symmetry axis to utilize the ac ground. The modulation scheme used for data transmission is orthogonal frequency-division multiplexing (OFDM), which is sensitive to nonlinear distortion. This means that the PA has to be optimized for high-output P rather than for saturated output power. To achieve a high P , a class-A PA was chosen. The PA draws 190 mA from a 3.7-V supply.

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Fig. 3. Output power versus input power sweep of a 100-MHz sine-wave signal.

Fig. 4. Receiver architecture of the 57–64-GHz front-end.

The transmitter chip was measured on-board. The transmitter was first measured with a 100-MHz sine-wave input. The transmitted 60.1-GHz signal was measured with a -band waveguide antenna with a gain of 22.5 dBi, a power sensor, and a power meter. The power at the output of the transmitter was calculated from the measured received power by subtracting the antenna gain and adding the free-space loss (62 dB at 0.5 m). Fig. 3 shows the measured output power for the swept input power. The calculated Tx conversion gain after 2.5 dB correction for the cable and balun loss is 33 dB. Saturated output power is 16.2 dBm and P is 12.6 dBm. The measured phase noise of the sine wave at 1-MHz offset is 97 dBc/Hz. The Tx consumes 1300 mW from three different supplies: 3.7, 3.3, and 2.5 V and has a size of 3.3 mm . The 60-GHz receiver also utilizes a sliding-IF architecture. Its building block diagram is shown in Fig. 4. A differential architecture is adapted from antenna to baseband because of its robustness with respect to bond wires and its common-mode rejection ability. The quadrature local-oscillator (LO) signals for the second down-conversion mixers are generated by a divide-by-four circuit in the PLL chain, which gives perfect I/Q signals because both I and Q signals respond only to the rising edge of the 48-GHz VCO output. The receiver front-end consists of a low-noise amplifier (LNA), a mixer, a PLL, and an IF demodulator. The LNA is a three-stage common emitter amplifier with 18-dB gain and 22-GHz bandwidth. The overall simulated noise figure (NF) is

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(a)

(b)

Fig. 7. LTCC transceiver module with mechanical support. (a) Antenna aperture. (b) Receiver and connectors. Fig. 5. Measured and simulated noise figure of the 60-GHz LNA.

and CMOS is comparable. Due to lower supply voltages, the power dissipation of 60-GHz CMOS RF chips is slightly lower. Concerning the chip architecture, the Tx and Rx functionalities could also be integrated into one chip, but there are some drawbacks to this solution. The single-chip solution would make the RF board design more difficult, because two antennas would have to be in close proximity and crosstalk could damage the LNA or deteriorate the performance. Additionally, it would require a 60-GHz T/R switch, but state-of-the-art 60-GHz SiGe switches are very lossy and come with low isolation. However, this challenge might be solved in the near future by implementing hybrid or monolithically integrated RF-MEMS switches [10], [11]. Fig. 6. Photograph of the 57–64-GHz SiGe BiCMOS receiver chip. RF-in ports on the left side and baseband IQ-out ports on the right. Size: 3.3 mm .

6.6 dB (NF of 4.5 dB, input loss of 0.6 dB, and contribution of later stages is 1.3 dB). Simulated and measured NFs are shown in Fig. 5. The measured NF is from 6.4 to 7.2 dB at the frequency band of 57 to 66 GHz, which agrees well with the simulated results. The 60-GHz mixer design features Gilbert cell topology, where output and load are optimized to match the 12 GHz of the IF band. Its simulated noise figure is 14 dB, which contributes only slightly to the overall noise performance of the receiver due to the high-gain LNA. The 12-GHz demodulator is designed to have a conversion gain of 50 dB with more than 30-dB gain control range. An SPI is introduced for the gain and IQ variable gain amplifier (VGA) mismatch control, thereby reducing the number of bond pads. The complete receiver analog front-end has a 78-dB conversion gain. Although the gain is very high, it is separated on three stages at 60 GHz, 12 GHz, and the baseband and, hence, does not pose a high risk for oscillations. The Rx consumes 980 mW from two different supplies: 3.3 and 2.5 V. Fig. 6 shows a micrograph of the 57–64-GHz receiver chip fabricated in SiGe BiCMOS technology. A detailed comparison of the performance of the chip solution presented here with other 60-GHz RF-IC designs is given in [9]. It shows that this chipset in 0.25- m SiGe BiCMOS technology is very competitive. The main advantage of SiGe BiCMOS is higher TX/PA output power, while the NF of receivers in SiGe

B. LTCC Integrated Antenna and LTCC RF Front-End The LTCC front-end includes the transceiver chips as well as the antenna elements and the blocking capacitors. A total of six LTCC layers are needed to implement the antenna structure with two additional layers for the integration into the Tx/Rx module. The front side of the LTCC module is used to place the RF/IF chips, which are mounted in a cavity and are shielded by a metal housing, and the baseband (BB) I/Q input/output connectors. The RF chip has a baseband bandwidth of 2.16 GHz. The antenna aperture is located on the backside of the LTCC module so that it becomes an integral part of the LTCC. Additionally, a passive heat sink is mounted on the antenna side, which also serves for mechanical support of the module. The complete LTCC RF front-end is shown in Fig. 7. The overall module dimensions of 29 mm 29 mm are well suited for the target application. 1) Antenna Design: The antenna comprises two LTCC-filled radiating cavities, which behave as aperture antennas, forming a small 2 1 array. The side walls of the cavities are realized with metal-filled vias. The cavities are tapered in width to increase the impedance bandwidth. The depth of each cavity is close to at 60 GHz. Each cavity is fed through a stripline, which acts as a probe to excite the cavity modes. This antenna structure yields a large bandwidth and a good decoupling of the radiating elements in the array. In order to be able to characterize the antenna as standalone element, a simplified version was designed and fabricated. It includes a transition to a WR-15 waveguide flange. The simulated antenna model including the fitting pins as well as the nylon screws to fix the waveguide feed is depicted in Fig. 8.

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(b)

Fig. 11. Measured radiation pattern at

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90 .

Fig. 8. (a) Empire XCcel simulation model, antenna with WR-15 flange. (b) Realized LTCC antenna with waveguide interface.

Fig. 12. Measured radiation pattern of the stand-alone antenna.

Fig. 9. Setup for the measurement of the reflection coefficient of a 2 sample.

2-array

Fig. 13. Simulation model of the bonding between the RF chip and LTCC module. Fig. 10. Finite-difference time-domain (FDTD) simulation and measurement of the reflection coefficient of a 2 1 array (including waveguide transition).

The setup for the measurement of the reflection coefficient using the waveguide variant is shown in Fig. 9. For the measurements, a WR-15 to coaxial adapter was used. The antenna integrated in the module yields a matching better than 10 dB over a bandwidth of 6 GHz, as shown in Fig. 10 [12]. The measured radiation patterns of the antenna prototype (without the transceiver circuit) for 90 for three different frequencies (58, 59, and 60 GHz) are also displayed in Fig. 11 [13]. A 3-D illustration of the radiation characteristics of the antenna is shown in Fig. 12. 2) Module Integration: In addition to the required chipsets, the LTCC module includes an LO, a mini-SMP connector for

an optional external oscillator, and a flat ribbon cable connector for SPI chip control signals. A balun is also needed for the transformation of the single-ended baseband signal to the differential input of the chip. The external baseband connection is performed through mini-SMP connectors. The differential RF ports of the RF chip are bonded to two parallel microstrip lines, followed by a transition to striplines that lead to the antennas, as illustrated in Fig. 13. Wire bonding was chosen for flexibility reasons to ease test measurements and modifications to the board setup. Moreover, the fabricated chips had not been verified for flip-chip mounting. Flip-chip mounting could still be used in combination with a proper cooler, which, however, would make it more difficult to access the chip for testing. To keep the bond wires as short as

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TABLE II MAIN CHARACTERISTICS OF THE RX AND TX MODULES

Fig. 14. Rx module with SPI interface board (on the left side) for controlling the chip and without RF chip housing.

TABLE III OFDM PHY LAYER PARAMETERS

possible and minimize the resulting mismatch, flat bond wires were used. Each path contains matching lines for proper impedance matching from the 50- microstrip lines at the output of the RF chip to the 37- striplines that feed the antennas. Indeed, technological limitations prevented the use of 50- striplines. The signals on the two lines have a phase difference of 180 . This symmetrical feeding allows for an optimized power transfer between the differential RF transceivers and the antenna without a balun. Table II summarizes the key parameters and the used components of the Rx and Tx modules. The realized module is fully functional. However, switching between four channels is not yet supported. Some interfaces including power supply and SPI signal are needed for connecting the module. Fig. 14 depicts a complete module including an SPI interface board. V. BASEBAND PROCESSOR AND MEDIUM-ACCESS CONTROLLER The challenges in this application for the baseband and medium access controller were: • seamless handover for redundancy; • QoS regarding latency and reliability; • high data throughput. The OFDM baseband processor supports modulation schemes from binary phase-shift keying (BPSK) to 64-QAM with convolutional coding and data rates up to 1.08 Gbps. The channel bandwidth for the used 256 subcarriers is about 350 MHz. Table III shows the main physical (PHY) layer parameters. The high data rate is only feasible with parallel processing of four samples and structural block parallelization. The biggest

impact appears in the receiver data path. Deinterleavers and Viterbi decoders have to be replicated 12 times and consume a considerable amount of resources. Detailed explanations can be found in [14] and [15]. The transceiver was fully integrated in a programmable logic (FPGA) platform with two Xilinx Virtex II PRO 100. It consumes all of the resources of both FPGAs. The analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) are connected with add-on boards to the signal processing part. The medium-access controller (MAC) coordinates the combined polling and time-division multiple-access (TDMA) scheme, which is required for the handover scenario of the demonstrator. Fig. 15 shows the structural overview of the MAC. The incoming Ethernet packets will be stored in the appropriate transmit buffer depending on the destination. The transmit buffer also aggregates these Ethernet packets into bigger MAC packets to reduce the MAC and PHY layer overhead. The aggregation results in higher MAC throughput. An immediate acknowledgement (ACK) supports retransmissions of damaged or lost packets to increase the robustness of the

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Fig. 15. MAC FPGA board structural overview.

Fig. 17. Baseband FPGA platform with add-on boards.

VI. USER INTERFACE SOFTWARE Fig. 16. Path switching between APs and seats.

system. The frame check sequence of received packets will be verified in the pre-stage of the receive buffer. Valid data packets are forwarded for disaggregation and finally delivered to the Ethernet switch. Received ACKs included in the MAC header will be sent to the transmit buffer. The corresponding MAC packet will be discarded, and the next one is prepared for transmit. The controller is based on a big state machine and organizes the protocol flow and provides the direction signal for the analog baseband switches used in the seat configuration. The TDMA scheme needs strong timing synchronization between both APs of the demonstrator due to the clock drift of the crystals on the FPGA boards. Only one AP has access to the medium at the same slot. There is no timing synchronization possible over the air due to the directional antennas. Therefore, a cable is used between the APs. Fig. 16 shows the switching scheme regarding the APs and seats. Each slot has a duration of a multiple of 4 ms with a short safety gap in between. This scheme allows a fast reaction on blocked paths. No connection reestablishment is necessary. The configuration and monitoring of the MAC state is supported by the User Datagram Protocol (UDP). The required UDP server and Address Resolution Protocol (ARP) replier are included in the integrated Ethernet switch. A protocol converter module gains access to a memory-like configuration and status interface. The MAC with the Gigabit Ethernet interface was fully integrated in a Virtex 4 FX60 FPGA add-on board. The integration of the MAC uses 50% of the FPGA’s logic resources and 99% of the built-in memory. Fig. 17 shows the FPGA platform with the DAC/ADC and MAC add-on boards. The BB processor and MAC processor of a transceiver implemented on the FPGA platform with high-speed ADCs and DACs and various interfaces, including 1-Gbps Ethernet, consume about 50 W. For an advanced version of the system demonstrator, it is planned to realize an application-specific integrated circuit (ASIC) implementation of the OFDM BB processor. It is estimated, that using an advanced ASIC technology, power dissipation of the BB processor and MAC processor can be reduced to below 1 W.

The user interface software uses the standard digital living network alliance (DLNA) protocol to dynamically find multimedia servers available in the backbone, allowing a distributed architecture to avoid single points of failure. The content of each server is discovered by means of DLNA and then merged, classified, and presented to the end user as if only a unique server would be available. This completely isolates the complex backbone architecture from the user. As soon as the user wants to reproduce any of the media, the server starts a unicast stream to the selected client. Transmission Control Protocol (TCP) streaming is performed, since there is a large amount of bandwidth available, which allows faster downloads and offers a better video experience for prerecorded media; in contrast to live streaming, where real time and low latency is desired and therefore UDP should be used. VII. ANTENNA-INSTALLED PERFORMANCE To analyze the impact of the surrounding material on the antenna pattern and to find the best placement of the antenna in the seat, an analysis of the antenna-installed performance in a passenger seat was performed by measurements in an anechoic chamber. The backrest of a passenger seat was mounted on a turntable and the LTCC antenna (see Fig. 8) was placed in different positions and configurations in the seat. A photograph of the backrest of an airplane passenger seat in the anechoic chamber is shown in Fig. 18. The antenna has a W-15 waveguide-interface and receives the radiated signal of a standard-gain horn antenna. With the rotation of the turntable, the pattern of the LTCC antenna integrated in the seat could be measured in elevation an azimuth. For the testing, the antenna was mounted in different positions relative to the seat cover and the supporting foam to analyze the influence of the surrounding material. The pattern in elevation and azimuth for the different positions were compared with the pattern of the uninstalled antenna (see Fig. 11). Two representative measurements for the installed antenna—installed, but not covered with foam and seat cover, and completely installed—are shown in Fig. 19. Peaks of attenuation were observed for discrete angles of the turntable. These are caused by reflections from the surface of the seat cover for

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Fig. 20. Azimuth antenna pattern with and without planar radome in front of the antenna. The distance between the antenna and radome is 3 mm and radomes with different thicknesses were tested. Inset: measurement arrangement.

Fig. 18. Backrest of an airplane passenger seat mounted on a turntable for measurements inside an anechoic chamber.

attenuation below 1.5 dB for normal incidence. Slight changes in the arrangement of the seat cover causes a shift of the angles where attenuation peaks are measured. In order to optimize the antenna performance integrated in the aircraft passenger seat, the antenna should not radiate parallel to the seat cover or through seams of the seat cover. Therefore, the top side of the passenger seat is the optimum choice for integration rather than the side. Furthermore, the rather fragile LTCC integrated antenna has to be protected from external impact (e.g., unintended mechanical load by passengers) with a radome for the integration inside the foam. Therefore, the effect of a planar radome in front of the antenna with three different thicknesses (1.2, 1.3, and 1.4 mm) was analyzed. Two different distances (3 and 10 mm) between the radome and the antenna were considered. The material of the radome is PEEKTM 450GL30 of the manufacturer Victrex, which is a thermoplastic material that is reinforced with glass fiber and qualified by many aircraft manufacturers. The size of the radome is large compared with the dimensions of the antenna. In Fig. 20, one can see the azimuth pattern of the antenna with radomes of various thicknesses 3 mm in front of the antenna and without a radome. It is evident that the radome and the thickness of the radome play no significant role for the antenna pattern. When the distance of the radome is increased to 10 mm, slightly sharper slopes can be observed. VIII. SEAT AND CEILING INTEGRATION IN CABIN MOCK-UP

Fig. 19. Representative measurement of the antenna pattern at one mounting position without foam and seat cover (dashed line) and completely installed (solid line).

shallow angles of incidence and by seams of the seat cover running across the antenna aperture. The seat material itself has

Two STTs and two user interfaces (touchscreens) were integrated into one row of seats to realize a redundant connection to two APs. An STT consists of one transmit-and-receive front-end with its separate power supply and control boards. Fig. 21 shows a photograph of the integrated STTs into a standard business-class aircraft seat. The STT baseband components (ADC and FPGA boards) are placed under the seats and inside the overhead compartments for the APs. The row of seats with the integrated STTs is placed between two aisles, and the positions of the APs are at a distance of 3 m,

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periodically checks the connectivity and buffer level of the different APs and clients. An algorithm analyzes the data provided by the access points and decides the route for each data packet individually. This allows, even with very small buffering on the client side, a perfect video experience when one of the two links is blocked. The graphical representation of the link monitor information provided by the wireless transceivers and used by the server to route the video stream is shown in Fig. 22 (bottom right). The first system tests resulted in a physical layer data rate of 240 Mbit/s with a QPSK modulation. This is limited by the ADCs and DACs used in the current system configuration. The latency achieved is lower than 1 ms, which is sufficient for this application.

Fig. 21. Integration of two STTs into a standard business class aircraft seat (left seat: uncovered; right seat: covered) in the cabin mock-up. Inset bottom right: link monitor information during data transmission.

X. CONCLUSION A prototype of a high-data-rate 57–64-GHz wireless communication system was specifically developed for the intended application and integrated for the first time into an aircraft cabin mock-up. All system components were developed and successfully evaluated during first installed performance tests in the mock-up. The next steps will be the miniaturization of the baseband hardware using ASICs and further system tests. ACKNOWLEDGMENT

(a)

(b)

Fig. 22. Access points behind the cabin ceiling panels in the cabin mock-up. (a) Covered by the ceiling panel. (b) Uncovered.

above these aisles and behind the glass-fiber reinforced plastic ceiling panels. Fig. 22 is a photograph of the APs hidden behind the ceiling panel and uncovered. IX. SYSTEM PERFORMANCE In the cabin communication system, the bandwidth requirements are typically asymmetric, since most of the data transfer happens in the downlink. Data sources are typically infrastructure elements (servers), and the destinations are the user terminals (clients). Nevertheless, a fast and reliable uplink connection is also required to allow new applications like video telephony in addition to the control and signaling messages. The demonstrated system is formed by two 60-GHz APs which forward the data coming from a wired server connection to the two clients on a TDMA basis over the air. This requires a total of four logical slots, reducing the theoretical maximum bandwidth needed to a fourth of the physical layer data rate. The uplink works on a polling basis. The APs ask each client for data in the corresponding slot. The client sends the data to the server via any of the two APs. However, the correct AP has to be chosen for the downlink in order to avoid unnecessary latencies or buffer overflow since they actively start the communication in each of the four slots. For this matter the server

The authors would like to thank Prof. W. Menzel and T. Chaloun, University of Ulm, Ulm, Germany, for support of the antenna installed-performance and cabin material measurements. REFERENCES [1] [Online]. Available: http://rockwellcollins.com/sitecore/content/Data/ Products/Cabin/Inflight_Entertainment_Systems/Paves3.aspx [2] [Online]. Available: http://www.qantas.com.au/travel/airlines/wireless-inflight-entertainment/au/en [3] V. Ziegler, B. Schulte, J. Sabater, S. Bovelli, J. Kunisch, K. Maulwurf, M. Martinez-Vazquez, C. Oikonomopoulos-Zachos, S. Glisic, M. Ehrig, and E. Grass, “Aircraft cabin-integrated 57–64 GHz WLAN communication system,” in Proc. IEEE Int. Microw. Symp., Montreal, QC, Canada, Jun. 17–22, 2012, pp. 1–3. [4] E. Grass, K. Tittelbach Helmrich, C.-S. Choi, F. Winkler, T. Ohlemueller, and R. Kraemer, “Communication systems operating in the 60 GHz ISM band: Overview,” Int. J. Microw. Wireless Technol., vol. 3, no. 2, pp. 89–97, 2011. [5] High Rate 60 GHz PHY, MAC and HDMI PAL, Standard ECMA-387, Dec. 2008, 1st ed.. [6] Standard for Information Technology, Part 15.3: Wireless Medium Access Control (MAC) and Physical Layer (PHY), Specifications for High Rate Wireless Personal Area Networks (WPANs), Amendment 2: Millimeter-wave-based Alternative Physical Layer Extension, IEEE P802.15.3c-2009. [7] Draft Standard for Information Technology, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Amendment 5: Enhancements for Very High Throughput in the 60 GHz Band, IEEE P802.11ad/D1.0. [8] B. Schulte, M. Peter, R. Felbecker, W. Keusgen, R. Steffen, H. Schumacher, M. Hellfeld, A. Barghouthi, S. Krone, F. Guderian, G. Fettweis, and V. Ziegler, “60 GHz applications and implementation aspects,” Int. J. Microw. Wireless Technol., vol. 3, no. 2, pp. 213–223. [9] S. Glisic, J. C. Scheytt, Y. Sun, F. Herzel, R. Wang, K. Schmalz, M. Elkhouly, and Ch.-S. Choi, “Fully-integrated 60 GHz transceiver in SiGe BiCMOS, RF modules, and 3.6 Gbit/s OFDM data transmission,” Int. J. Microw. Wireless Technol., vol. 3, no. 2, pp. 139–145, 2011.

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[10] B. Schönlinner, A. Stehle, C. Siegel, W. Gautier, B. Schulte, S. Figur, U. Prechtel, and V. Ziegler, “The low-complexity RF MEMS switch at EADS: An overview,” Int. J. Microw. Wireless Technol., vol. 3, no. 5, pp. 499–508, 2011. [11] M. Kaynak, K. E. Ehwald, J. Drews, R. Scholz, F. Korndorfer, D. Knoll, B. Tillack, R. Barth, M. Birkholz, K. Schulz, Y. M. Sun, D. Wolansky, S. Leidich, S. Kurth, and Y. Gurbuz, “BEOL embedded RF-MEMS switch for mm-wave applications,” in Proc. IEEE Int. Electron Device Meeting, Baltimore, MD, Dec. 7–9, 2009, pp. 1–4. [12] C. Oikonomopoulos-Zachos and M. Martínez Vázquez, “Effect of technological tolerances in the design of a 60 GHz LTCC antenna,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Toronto, ON, Canada, Jul. 11–17, 2010, pp. 1–4. [13] C. Oikonomopoulos-Zachos, D. Titz, M. Martínez-Vázquez, F. Ferrero, C. Luxey, and G. Jacquemod, “Accurate characterisation of a 60 GHz antenna on LTCC substrate,” in Proc. 5th Eur. Conf. Antennas Propagation, Apr. 11–15, 2011, pp. 3117–3121. [14] M. Piz, M. Krstic, M. Ehrig, and E. Grass, “An OFDM baseband receiver for short-range communication at 60 GHz,” in Proc. IEEE Int. Symp. Circuits Syst., 2009, pp. 409–412. [15] M. Krstic, M. Piz, and E. Grass:, “60 GHz datapath processor for 1 Gbit/s,” in Proc. VLSI-SOC, Oct. 13-15, 2008, pp. 156–159.

Volker Ziegler (M’00–SM’09) was born in 1971 in Tuebingen, Germany. He received the Dipl.-Ing. degree in electrical engineering and Dr.-Ing. degree (with honors) from the University of Ulm, Ulm, Germany, in 1997 and 2001, respectively. He was member of the “Knowledge Exchange Group for Research and Technology” with DaimlerChrysler AG, Stuttgart, Germany, from 2001 to 2002. During this trainee period, he worked at the University of Michigan, Ann Arbor, on the design of GaN high-power MMICs and at United Monolithic Semiconductors, Orsay, France, on the modeling and characterization of III-V semiconductor devices. In 2003, he joined EADS Innovation Works, Ottobrunn, Germany, as a Research Engineer. Since 2007, he is an EADS Expert for “Microwave Technologies and Systems” responsible for the acquisition and management of national and international research projects in the field of key microwave technologies for advanced radar and communication systems. He served twice as an associate editor for the International Journal of Microwave and Wireless Technologies and is a member of the Technical Program Committee for the European Microwave Week. He authored or coauthored more than 60 papers, holds nine patents, and is an industrial advisor of the “Component Technical Board on Microwaves” for the European Space Agency. Dr. Ziegler is member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Technical Coordinating Committee 21 on RF-MEMS and of the IEEE MTT-S Antennas and Propagation German Chapter Executive Board.

Benedikt Schulte received the Diploma degree in electrical engineering from the University of Siegen, Siegen, Germany, in 2008. He is currently working toward the Ph.D. degree in electrical engineering. Then, he joined EADS Innovation Works, Ottobrunn, Germany. His research interests include highly integrated microwave front-ends (e.g., tunable filters and electronic steerable antenna arrays) for communication and radar systems. Since 2012, he has been a Development Engineer and Project Manager for radar systems with Astyx GmbH, Ottobrunn.

Jürgen Kunisch received the Dipl.-Ing. and Dr.-Ing. degree (with honors) in electrical engineering from the University of Duisburg, Duisburg, Germany, in 1989 and 1994, respectively. Currently, he is heading the wave propagation and radar methods section of IMST GmbH, Kamp-Lintfort, Germany. His working areas include radar signal processing, the physical layer of mobile communication and localization systems, and, in particular, measuring and modeling of radio wave propagation.

Kai Maulwurf was born in Wesel, Germany, in 1980. He received the Diploma degree in electrical engineering from the Rheinische Fachhochschule Köln, Köln, Germany, in 2005. He is currently with the RF-Modules Group, Department of RF Circuits and System Integration, IMST GmbH, Kamp-Lintfort, Germany. His work includes the design, simulation, and measurements of analog front-end modules up to 77 GHz for communication systems and radar applications.

Marta Martínez-Vázquez (M’06–SM’09) was born in Santiago de Compostela, Spain, in 1973. She received the M.Sc. and Ph.D. degrees in telecommunication engineering from the Universidad Politécnica de Valencia, Valencia, Spain, in 1997 and 2003, respectively. In 1999 she was granted a fellowship from the Pedro Barrié de la Maza Foundation for postgraduate research at IMST GmbH, in Germany. Since 2000, she has bee a full-time Staff Member with the Antennas and EM Modelling Department, IMST GmbH, Kamp-Lintfort, Germany. She has authored and coauthored over 50 publications, including books, book chapters, journal and conference papers, and patents. Her research interests include the design and applications of antennas for mobile communications, planar arrays, sensors, and RF systems. Dr. Martínez-Vázquez was awarded the 2004 Best Ph.D. award of the Universidad Politécnica de Valencia for her dissertation on small multiband antennas for handheld terminals. She is the chair of the COST IC1102 Action “Versatile, Integrated and Signal-aware Technologies for Antennas (VISTA). Previously, she was a member of the Executive Board of the ACE (Antennas Centre of Excellence) Network of Excellence (2004–2007) and the leader of its small antennas activity, and the vice-chair of the COST IC0603 Action “Antenna Sensors and Systems for Information Society Technologies” (2007–2011). She is a member of the Administrative Committee of the IEEE Antennas and Propagation Society, of the Board of Directors of the European Association of Antennas and Propagation (EurAAP), and of the Technical Advisory Panel for the Antennas and Propagation Professional Network of IET. She is currently a Distinguished Lecturer for the IEEE Antennas and Propagation Society, an editor of the IEEE Antennas and Propagation Magazine, an associate editor of the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, and a member of the editorial board of the Radioengineering Journal.

Christos Oikonomopoulos-Zachos (M’09) was born in Volos, Greece, in 1976. He received the Dipl.-Ing. and Ph.D. degrees in electrical engineering from the RWTH Aachen University, Aachen, Germany, in 2003 and 2010, respectively. From 2003 until 2008, he was a Scientific Assistant with the Department of High Frequency Technology, RWTH Aachen University, Aachen, Germany. Since 2009, he has been with the Department of Antennas and EM Modelling, IMST GmbH, Kamp-Lintfort, Germany. He is the author of several papers in scientific conferences and journals. His current interests include MIMO antenna systems, LTCC technology, mobile communications antennas, and automotive antennas.

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Srdjan Glisic received the B.S. degree in electrical engineering from the Faculty of Electronic Engineering, Nis, Serbia, in 2000, and the Ph.D. degree from Brandenburgische Technische Universität Cottbus, Cottbus, Germany, in 2010. He joined the Circuit Design Department, IHP, Frankfurt Oder, Germany, in 2003, where he is involved in projects on 60-GHz wireless communication and automotive radar in 77-GHz frequency range. He works mainly on voltage-controlled oscillators, phase-locked loops, and power amplifiers, as well as printed circuit board design and system integration.

Marcus Ehrig received the Diploma degree in information science from the Humboldt University, Berlin, Germany, in 2006. He joined the Wireless Broadband Communication Group, IHP, Frankfurt Oder, Germany, in 2006. His research interests include wireless communication systems, digital signal processing architectures, and high-performance hardware architectures.

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Eckhard Grass received the Dr.-Ing. degree in electronics from the Humboldt University, Berlin, Germany, in 1993. He was a Visiting Research Fellow with Loughborough University, U.K., from 1993 to 1995, and a Senior Lecturer in Microelectronics with the University of Westminster, London, U.K., from 1995 to 1999. Since 1999, he has been with IHP, Frankfurt Oder, Germany, , leading several projects on the implementation of wireless broadband communication systems. Since 2007, he has been a team leader of the Wireless Broadband Communications Group at IHP. In addition, he has been a Professor with the Department of Informatics, Humboldt University, Berlin, Germany, since 2011. He has authored and coauthored approximately 80 papers at international conferences and in international journals. His research topics include wireless communication systems, asynchronous circuit design, and digital signal-processing architectures.

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GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion José A. García, Member, IEEE, Reinel Marante, Student Member, IEEE, and María de las Nieves Ruiz Lavín, Student Member, IEEE

Abstract—In this paper, the design and performance of class E resonant topologies for dc/dc power conversion at UHFs are considered. Combining the use of RF gallium–nitride HEMT devices, both for the inverter and synchronous rectifier, with highlumped-element terminating networks, peak efficiency values over 70% may be obtained. Control strategies based on carrier bursting, switching frequency modulation, or outphasing are also shown to be feasible. Taking advantage of their improved dynamic response, when compared to low-frequency more traditional switched-mode converters, a class E polar transmitter for the EDGE standard has been designed and tested at 770 MHz, offering an average global efficiency over 46% at 4.3 W of output power, through RF-based amplitude and phase constituting branches. Finally, the potential of such a high frequency of operation in terms of power density is explored, absorbing undesired coil parasitics for the original LC series interconnecting network in a 1-GHz design methodology. Index Terms—Class E, dc/dc power converters, field-effect transistors (FETs), gallium–nitride (GaN), high power amplifiers (PAs), phase control, predistortion, pulsewidth modulation (PWM), radio transmitters, rectifiers, resonant inverters, switching converters, UHF circuits, zero voltage switching (ZVS).

I. INTRODUCTION

M

ODERN POWER electronics applications are continuously demanding power-efficient converting systems with a very fast transient response and improved control bandwidth. That has recently been the case, for instance, of the envelope modulator in envelope tracking (ET), envelope elimination and restoration (EER), or hybrid ET/EER wireless transmitters [1], where the amplitude component of a high data rate digitally-modulated signal (multicarrier WCDMA, orthogonal frequency division multiplexing (OFDM), or similar), with tens of megahertz of spectral content, has to be linearly reproduced at the output. Together with the interest in miniaturization, associated to the reduction in the required energy storage and the

Manuscript received July 10, 2012; revised September 24, 2012; accepted September 26, 2012. Date of publication October 25, 2012; date of current version December 13, 2012. This work was supported by the Spanish Ministries MICINN and MINECO through the FEDER co-funded Project TEC2011-29126-C03-01 and Project CSD2008-00068. The work of J. A. García was supported under a Mode A Professorship Mobility Grant (PR2010-0202). The work of R. Marante was supported under a MAEC-AECID Doctorate Grant (0000524566). This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012. The authors are with the Department of Communications Engineering, University of Cantabria, 39005 Santander, Spain (e-mail: joseangel. [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2012.2222043

use of smaller valued and sized passive components, as to reach the power supply-in-package (PSiP) and power supply-on-chip (PwrSoC) ultimate targets [2], a great motivation has appeared on the operation of power converters at switching frequencies quite over the 0.1–10-MHz range of today’s figures. Achieving competitive efficiency values in dc/dc converters at VHF, UHF or higher frequency bands, requires keeping frequency-dependent switching loss mechanisms under control. Using zero voltage switching (ZVS) [3], they may be alleviated by mitigating the voltage/current overlap while also forcing a low voltage across the semiconductor terminals during the ON/ OFF transitions, also resulting in a reduction of the electromagnetic interference (EMI) associated to hard-switched more traditional converters [4]. Several solutions at HF and VHF bands have appeared during the last years [5] based on class E [6], or more recently, in class topologies [7]. Operation at higher frequencies was also explored in the past [8], but restricted to small power levels, mainly due to the nonavailability of appropriately fast power transistors and Schottky diodes by that time. In this paper, the implementation of UHF resonant dc/dc power converters, following class E topologies, is considered. The use of RF depletion-mode gallium–nitride (GaN) HEMT devices, both for the inverter and the synchronous (active) rectifier, together with high- lumped-element terminating networks allow improving the operating bandwidth while also preserving a high efficiency. The output voltage is shown to be perfectly controlled through different techniques, each with its advantages and limitations, finding the improvement of the dynamic response application in a wireless high-efficiency transmitter. A solution is also considered in the miniaturization direction. In Section II, the selected topology is introduced, described, and adapted according to UHF particular implementation restrictions with GaN transistors. Characterization results are then presented in Section III under different output voltage control strategies. Special attention is put in the design of an alternative outphasing scheme, introducing recent advances on class E load modulation techniques. The use of a carrier bursting converter as envelope modulator for an EDGE standard wireless polar transmitter is considered in Section IV, while a small sized topology is finally proposed in Section V. II. CLASS E DC/DC CONVERTER With the aim of operating at hundreds of kilohertz or even megahertz frequencies, alternative transistor-based topologies to hard-switched converters were proposed by power supply specialists in the 1980s [9]. As turn-on and turn-off losses were

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by the device (including the capacitance) at the fundamental frequency. Under these conditions, the inverter was proved to be seen by its dc supply as a load with value (2)

Fig. 1. (a) Class E inverter or PA. (b) Its TR dual, a class E synchronous rectifier, together with: (c) basic class E dc/dc converter obtained when cascading (a) and (b).

associated to the employed rectangular waveforms, the introduction of a resonant circuit helped shaping either a sinusoidal voltage or a sinusoidal current. Combining a dc/ac resonant inverter and a high-frequency rectifier, a resonant converter first transforms the dc input power into a controlled ac power, to then turn it back into the desired dc output [3], [4].

From the inverter circuit, applying the time reversal (TR) duality principle, as described in [16], the class E rectifier of Fig. 1(b) may be easily derived. In this case, optimum operation is obtained for , , and values, as in (1a), (1c), and (2), respectively, while the required phase shift, , between the gate-to-source and the drain-to-source voltage waveforms should be set to 180 as to obtain the desired synchronization. The class E rectifier, as inverter TR dual, would then appear to its ac excitation as a perfectly resistive load , following (1b). The class E dc/dc converter of Fig. 1(c) results from cascading the above-described circuits. The rectifier provides by itself the load resistance required by the inverter so both of them may operate under the desired soft-switching conditions without adding any further element for the interconnection. Combining in series the two resonant circuits, the overall reactance to be presented by the resulting LC combination [16] should then be

A. Original Topology

(3)

Conceived as a class E RF power amplifier (RF PA) in [10], the idea of using ZVS and zero voltage derivative switching (ZVDS) for the inverter in resonant power conversion is due to Gutmann [11], while a deeper insight into its operation was later provided in [12]. Forcing soft-switching conditions not only for the inverter, but also for the rectifier, the double class E or class E converter was proposed by Kazimierczuk and Jozwik in [13], [14]. One of its many possible topologies [13] is presented in Fig. 1, where the rectification is of active or synchronous type. At high operating frequencies, UHF and beyond, fast enough Schottky diodes able of handling high current and voltage levels are rarely available, which is the reason why a transistor-based rectifier may be the only choice. The class E inverter of Fig. 1(a) was analyzed in detail in [15], assuming an infinite choke inductance, , in order to consider the device biasing branch as a dc current source, and a high enough loaded quality factor for the resonant circuit as to assure the current through it is a sinusoid at the driving signal frequency. Tuning the LC series resonant circuit slightly below the switching frequency, the optimum conditions, defined as those resulting in the ideal 100% efficient operation with maximum output power (according to the voltage and current restrictions imposed by the device characteristics), were found by Raab [15] to be (1a) (1b) (1c) being the switching duty cycle, while and are with the real and imaginary components of the impedance to be seen

For an ideal lossless operation, the output dc voltage would be equal to the input biasing value, while the dc load offered by the converter to its power supply would be exactly its load resistance . B. Device Model and Simulations Following this basic topology and concept, a packaged GaN HEMT from Cree Inc., Durham, NC (the CGH35030) was selected to be employed as the switching element. Besides this technology offering a very low value for the on-state resistance , its high breakdown output capacitance product, voltage 120 V allows alleviating the transistor stress associated to the voltage peaking waveform typical of a class E mode of operation. In order to construct a very simple model of the device as a switch, the ON state resistance was estimated from the low drain voltage slope of the measured I/V curves at high values, as represented in Fig. 2(a). For the equivalent frequency-dependent output capacitance, the parameter was measured in Fig. 2(b) at V (the voltage value initially selected for operation) and for a slightly below pinch-off, just before observing any significant increase in the output conductance. With this model, and forcing the required conditions for both the inverting and the rectifying devices, the class E topology was evaluated in terms of the switching frequency through harmonic balance (HB) simulations. The converter dc load and the interconnecting reactance were carefully adjusted according to (2) and (3), respectively, while open-circuit conditions were implemented at both drain terminals to the second- and third-order harmonics. The precise phase-shifting angle between the gate driving signals, required for assuring the desired coherent or

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Fig. 2. Estimated values for and from the sured I/V curves and (b)

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. (a) extracted from the meaparameter.

Fig. 3. Evolution of: output voltage (—) and drain efficiency (- -) with the switching frequency as obtained from HB simulations.

synchronous operation of the rectifier, was also set at each frequency point. In Fig. 3, the obtained evolution for the output dc voltage and drain efficiency are plotted. The efficiency figure was simply computed as in (4) with and representing the output and input dc power, respectively, (4) As expected, the efficiency figure reduces with frequency, staying above 80% up to 1 GHz. Considering the simplicity of the model, as well as the perfectly ideal terminating conditions implemented in the simulations, the real performance would be probably below these predicted curves. The design frequency

Fig. 4. Drain voltage and current waveforms for the: (a) inverting and (b) rectifying device, as obtained from HB simulations. The observed ringing may be ameliorated with the number of harmonics.

was then selected to be 780 MHz since the maximum frequency for optimum class E operation [17], [18] was estimated from the extracted to be around this value. The drain voltage and current waveforms, obtained from HB simulations at 780 MHz, are represented in Fig. 4. The voltage waveforms at the rectifying device in Fig. 4(b), as theoretically described [13], [16], are time-reversed versions of those for the inverter in Fig. 4(a). When one transistor is in its conduction state, the other is not. The ZVS and ZVDS conditions may be also appreciated, in the device transitions from OFF to ON (inverter) or from ON to OFF (rectifier). When turned on, the rectifying GaN HEMT operates in the third quadrant of its I/V characteristics, as it should provide power to the dc load. Most available nonlinear models, using a hyperbolic tangent function over as part of the equation, fail in accurately reproducing this “inverse” operating region. C. UHF Converter Design As the simple LC series network of Fig. 1 may turn inappropriate for RF operation, due to the undesired reactive parasitics generally associated to the coil and the capacitor, a multiharmonic terminating network was proposed in [19] as a lumpedelement version of the widely used microwave transmission line topology suggested in [20]. Based on this technique, the topology selected for the UHF converter and already introduced in [21] is reproduced in Fig. 5. Using Air Core “Spring” series inductors from Coilcraft, Cary, IL, and 100-B multilayer capacitors from ATC, Huntington Station, NY (values included

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Fig. 6. Output voltage (—) and efficiency (- -) versus the switching frequency V . for a CW excitation

Fig. 5. Simplified schematic of the UHF converter from [21].

frequency components as a short, excess losses could appear in the reproduction of wideband communication signal envelopes, as exemplified with a WCDMA format in [21].

TABLE I LUMPED ELEMENT VALUES IN THE CONVERTER SCHEMATIC

B. Output Voltage Control Through Frequency Modulation (FM) in Table I), the desired drain termination at the fundamental, second, and third harmonics were forced. A commercial hybrid coupler from Anaren, East Syracuse, NY, allowed distributing the gate excitations with the required phase shift. A photograph with implementation details may be also found in [21]. III. DC/DC CONVERTER PERFORMANCE Considering the overall efficiency, , as the figure of merit, where the required RF gate driving power, , is accounted for as in (5), a peak value of 72% was reported in [21], in the state-of-the-art for dc/dc converters in this frequency band (5)

A. Output Voltage Control Through Carrier Bursting In [21], a pulsewidth modulation (PWM), over the envelope of the gate driving signal (an ON/OFF type of output voltage control strategy [5]) was proposed. This mode of operation, with bursts of the carrier exciting the device gate terminals, has been also suggested for high-efficiency transmitters [22]. The switching frequency and its optimum duty cycle, , were kept fixed as to have switching losses under control. According to the reported evolution of output voltage and overall efficiency versus the envelope duty cycle, for a pulse repetition frequency of 500 kHz, a 3.7:1 control range could be perfectly covered with [21]. Being that the duty cycle to reconstructed voltage characteristic is nearly linear, such coding results are appropriate for reproducing dynamic variations with high fidelity. However, as the efficiency figure started degrading when increasing the pulse repetition frequency over a few tens of megahertz, mainly due to the highly demanding requirements for terminating the rectifying circuit at the carrier frequency as an open, while at the PWM

Other control techniques may offer alternative performance to PWM, as described in detail along this section and Section III-C. Attending to the measured evolution of efficiency and dc voltage, reproduced from [21] in Fig. 6, the switching frequency may be used as control variable instead of the envelope duty cycle. Proposed with the original topology in [13] and [14], an advantage may be taken from the reduction in the output voltage with frequency, typical of class E operation, as to code the desired voltage variations using FM of the gate driving signals. A maximum value of 72% could be obtained for a voltage 0.83 times the peak value, while the efficiency could be kept over 50% for a 1.9:1 voltage relation (corresponding to a peak-to-average power ratio (PAPR) of 5.6 dB, if thinking of its possible use as an envelope modulator). Although for such specific application, the efficiency would be preferred to peak at a lower voltage value, this strategy would avoid the impact of a reconstruction filter in terms of the dynamic response. C. Output Voltage Control Through Outphasing A third possible alternative for output voltage control, also employed for low-frequency dc/dc converters using class D or class DE topologies, is based on phase coding. Following the outphasing principle [23], two amplifiers are combined in a phase controlled inverting topology, followed by a rectifier. Advantage is usually taken from class D relative independence on the appearance of reactive components in the load. At the frequencies of our interest, where single-switch inverters are preferred, the impact of a non purely resistive termination at the inputs of a Chireix combiner may seriously degrade the performance of class A-, AB-, B-, C-, F-based or inverse F-based outphasing transmitters [24]. However, as it has been recently proven in [25] that is not necessarily the case for the class E topology. If properly transforming the load modulation paths, imposed by the combiner, into impedance loci at the drain terminals as close as possible to the optimum, where

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Fig. 7. Class E PA load–pull simulation including the output power and efficiency circles. The transformed impedance trajectories due to the combiner and the transmission line are also included.

Fig. 8. Schematic for the proposed UHF class E outphasing converter. Added lumped element values have been tabulated.

the ZVS condition may still be kept, through the addition of a carefully selected length of transmission line, the output power may be controlled while also conserving a high efficiency. Impressive results, following this strategy, have been reported for a wireless transmitter in [26]. Based on these studies and using the simplified switch model of Section II-B, a load–pull simulation at the fundamental was performed over the basic class E inverting topology of Fig. 1(a) at 780 MHz. Open-circuit terminations were forced at the second and third harmonics. The efficiency and output power circles are represented in Fig. 7, together with the trajectories to be obtained after properly transforming the impedance at both inputs of a simple reactive combiner with (see Fig. 8 for details). From this very simple simulation, an efficiency value over 80% could be expected for such an outphasing class E inverter along a power range greater than 8 dB. Based on these results, an alternative class E dc/dc converter to the one in [21] has been designed, following the schematic represented in Fig. 8. Two class E UHF PAs are asymmetrically combined through a reactive lumped-element topology and lengths of transmission line, constituting an outphasing inverter, followed by a class E rectifier. As when controlling the inverter output power, the resulting phase component of the RF (our ac) signal also varies with the outphasing angle, the phase

Fig. 9. Photograph with details of the UHF dc/dc converter, implementing the outphasing principle, and the employed test setup.

of the rectifier gate driving excitation would need to be consequently adjusted. A possible solution to this problem comes from taking a sample of the RF signal at the rectifier input to excite its device gate terminal. This sample should be correctly dimensioned as to force a switched-mode operation of the rectifier over a range as wide as possible. To avoid device damage at high power values, the resistance in its gate dc path may be correctly dimensioned in such a way that the gate-to-source voltage is reduced with respect to the applied biasing value when a small rectifying current appears at this terminal. In the proposed design, a small valued capacitor, , was used to take the sample, followed by the introduction of a network in the drain-to-gate interconnecting branch as to assure the appropriate phasing between the drain-to-source and gate-to-source voltages. Since the selected GaN HEMT is able to provide a very high gain at this frequency band, close to 20 dB, the impact on overall efficiency when taking such a small sample of the inverter ac output (the rectifier ac excitation) may be neglected. In Fig. 9, a photograph with details of this alternative double class E UHF converter, implementing the outphasing control voltage technique, is presented. No special attention was paid to produce a compact design, only to validate the topology. After characterizing the converter in terms of the outphasing angle, the output dc voltage and the overall efficiency have been represented in Fig. 10. A peak overall efficiency, also of 72%, has been obtained, but in this case for an output voltage 1.52 times below the maximum (corresponding to a 3.66-dB PAPR signal if thinking again on an envelope modulating application). The overall efficiency was kept over 50% for a 2:1 voltage control range. Although this range is reduced with respect to the results using the carrier bursting control technique, no reconstruction filter is here required. This makes this topology highly attractive in terms of the dynamic response. Through a careful selection of the reactance value and the use of an alternative solution for the rectifier gate driving signal, the voltage range might be extended as to reproduce signals with a higher PAPR.

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Fig. 10. Measured output voltage (—) and efficiency profiles (- -) versus the V and MHz. outphasing angle at

Fig. 12. Photograph with details of the implemented EDGE class E polar transmitter at 770 MHz.

Fig. 11. Diagram of the proposed UHF class E polar transmitter.

IV. CLASS E POLAR TRANSMITTER In order to test the potential of the carrier bursting class E converter of [21] in a real fast response application, as the above-mentioned bias adaptation wireless transmitters, a polar architecture has been selected. Since in a pure EER technique, the load impedance presented by the RF PA stays constant, there would be no need for regulating the converter output voltage despite its finite output impedance. Such regulation would be instead required in ET or hybrid ET/EER schemes. Taking also into account its bandwidth limitations, in terms of efficiency, related to the minimum required ratio to be conserved between the desired converter frequency response and the pulse repetition frequency (for PWM coding such voltage variations), as well as between this frequency and the carrier, an EDGE standard signal was selected. Having a moderate 200-kHz bandwidth, a 3.8-dB PAPR and a hole in its constellation, to avoid the feedthrough effect, this format is certainly amenable for polar transmission. A. UHF Polar Transmitting Scheme In Fig. 11, a simplified diagram of the proposed class E polar transmitter is represented. The class E resonant power converter is used to high level amplitude modulate a class E RF PA, in an analogous way to [27], excited with a constant-envelope phase modulated (PM) signal. The same carrier frequency is used, both for the PM and amplitude modulated (AM) branches, resulting in a fully RF-based implementation. One of the advantages of handling the envelope with an RF switching frequency is the reduced size of the implemented transmitter. In Fig. 12, a photograph with details of the RF part of the scheme may be appreciated. Three similar GaN HEMT devices, the CGH35030 from Cree Inc., are employed, two for the converter plus the one for the RF PA. The Pi capacitor–inductor–capacitor (CLC) reconstruction filter, with a 1-MHz

Fig. 13. to AM, to PM, and PAE static profiles for the class E RF PA. The EDGE envelope pdf function has also been plotted.

bandwidth and a maximally flat response, may also be distinguished. A 5-MHz pulse repetition frequency was employed for PWM coding the envelope variations. Since this frequency is quite below the carrier value, optimum rectifier terminations are possible. A second advantage of using this type of converter has to do with the correction of the differential delay between the AM and PM paths, one of the main nonlinear distortion sources in this type of architectures [28], [29]. Being that the AM component is also processed at the frequency used for the PM modulation, the differential delay is not significant at all. B. RF PA Stage For the RF PA, a stage similar to those integrating the converter has been selected. In Fig. 13, the measured static (with continuous wave (CW) RF excitation) to AM and to PM profiles are plotted, together with the probability density function (pdf), for the EDGE AM component and the power-added efficiency (PAE) evolution. A peak drain voltage value of 28 V was assumed. As is typical of class E operation [30], the most significant part of the envelope variation coincides with a nearly linear amplitude characteristic and a minor undesired phase modulation. Although the voltage and current waveforms have not been measured, these profiles may show

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TABLE II CLASS E TRANSMITTER FIGURES OF MERIT

Fig. 14. Diagram representation of the implemented DPD.

Fig. 15. Spectrum of the output signal, as compared to the original.

that the device is operating close to the desired ZVS and ZVDS conditions. Also taking into account the nearly linear duty cycle-to-AM characteristic measured for the class E converter in [21], a low predistortion effort could be required for transmitter linearization. Most of the envelope also fits in the region where the PAE is over 75%, which is the reason why a high average figure could be expected. C. DPD and Characterization Results After implementing the transmitter, a static characterization of output amplitude, , and phase variations, , with the envelope voltage, , was made (see Fig. 11 for notation). The input dc biasing voltage was fixed to 35 V, as to obtain a peak voltage at the converter output close to 28 V. A simple memoryless digital predistortion (DPD), based on [31], was then implemented as a lookup table (LUT) in order to reproduce the desired signal. As described in Fig. 14, the digitally generated amplitude component, , should include corrections to the AM-to-AM profile, including PWM modulation, dc/dc converter, and RF PA to AM nonlinearities. After that, the parasitic phase variations, , to be introduced by the AM modulating signal, from the characteristic in Fig. 13, were digitally subtracted from the desired PM component, . Once this simple predistortion strategy was applied, the spectrum of the output EDGE modulated signal was compared to the spectrum of the original version in Fig. 15. As may be appreciated, the recovered signal nearly fits the original. Out-of-band emission components were also measured at 5 MHz from the carrier and 55 dBc below its level. They are due to the PWM spectral components and the attenuation offered by the implemented reconstruction filter.

A summary of the measured output power, linearity, and efficiency figures is also included in Table II. The linearity specifications, 58 dBc at 400 kHz and 60 dBc at 600 kHz, are satisfied with an average transmitter efficiency figure over 46% (including the envelope modulator and RF PA). In these specific operating conditions, the average efficiency of the dc/dc converter was estimated to be over 60%. Attending to these results, appropriately dimensioning a class E power converting topology, a linear reproduction of a timevarying voltage envelope may be assured with low losses. If interested in efficiently handling signals with a wider envelope, such as WCDMA, long-term evolution (LTE), or similar, using this particular PWM resonant converter, a pulse repetition frequency of at least 100 MHz would be required. If using a higher carrier switching frequency, such as the 2.14 GHz required for base stations, the desired filter terminations would be feasible at the expense of a reduction in the achievable peak efficiency value (at least for the devices employed here). V. UHF POWER CONVERSION FOR MINIATURIZATION Having described the benefits of a UHF power converter in terms of frequency response enhancement, attention may be paid to the second benefit of a high-frequency conversion for power density improvement (size and weight reduction). The above proposed implementations are not exactly compact, mainly due to the selection of a multiharmonic network to properly terminate the inverting and rectifying devices, as well as the use of packaged versions for the transistors. A. LC Series Class E Converter Using Coil Self-Resonance To reduce the footprint and volume, the original LC series topology in [13] and [14] is a very attractive candidate. If taking advantage of the lumped-element parasitics, selecting a highcoil with a self-resonant frequency between the second and third harmonic, while carefully tuning the capacitance value as to provide the desired reactance of (3), the converter size could be significantly reduced. After characterizing, as in Section II-B, a die GaN HEMT with similar power capability, the CGH60030, also from Cree Inc., a simple network with an 8-nH Air Core “Spring” inductor from Coilcraft and two 8.2-pF 100 B ATC capacitors was adjusted. In Fig. 16, the evolution with frequency of the impedance as seen in one of its port, when loading the other with the desired ac resistive component is shown. As can be appreciated, the impedance at the fundamental frequency nearly fits the desired value, while the second- and third-order harmonic terminations are relatively close to the open-circuit condition thanks to the coil parasitic capacitance.

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TABLE III STATE-OF-THE-ART HIGH-FREQUENCY DC/DC CONVERTERS

B. Measured Performance Fig. 16. Measured evolution with frequency of one-port impedance, when . loading the other with the optimum resistance value,

The characterization results in terms of frequency are finally represented in Fig. 18. A good performance has been obtained, with a peak overall efficiency over 70%, through a much more compact and simple implementation. The voltage and efficiency profiles measured versus the duty cycle approximately followed those reported for the converter in [21]. Frequency or carrier bursting modulation for output voltage control would also be feasible. VI. CONCLUSION

Fig. 17. Photograph with magnified details of the miniaturized implementation at 1 GHz.

Fig. 18. Measured output voltage (—) and efficiency (- -) versus the switching V for the converter in Fig. 17. frequency at

In Fig. 17, a photograph of the suggested 1-GHz implementation is shown. The input and output dc networks have been included, as well as gate matching capacitors. The gate driving signal was externally split using a commercial in-phase power divider, also from Anaren. The desired phasing between the inverter and rectifier excitations was set by adding a few SMA transitions. The gate biasing voltage was also applied to both die devices through an external bias tee.

Class E resonant topologies for dc/dc power conversion at UHFs have been designed and characterized in this paper, considering their benefits for improving the response speed and power density over current lower frequency solutions. In the first case, a class E polar transmitting application for the EDGE standard has been proposed and tested at 770 MHz, offering an average global efficiency of 46% for more than 4 W of output power, with amplitude and phase branches fully implemented at the carrier frequency. Further considerations for obtaining a higher bandwidth have been also suggested, such as the use of an outphasing output voltage control strategy. In the miniaturization direction, a compact implementation, taking advantage of passive element parasitics and die device versions, has been also proposed. A peak value for the overall conversion efficiency over 70% has been measured, at 12.4 W of output power and 1 GHz. Comparing this work with previously published converters (see Table III), the obtained efficiency results are in the state-of-the-art according to the switching frequency and power level. Although the employed GaN HEMTs have not been conceived for this mode of operation and the efficiency figures are not currently competitive with more traditional kilohertz converters, the great potential of RF conversion using this technology has been proven. ACKNOWLEDGMENT Author J. A. García wishes to acknowledge all the advice and suggestions on the treated topics received from Prof. Z. Popović and Prof. D. Maksimovic, both with the University of Colorado at Boulder, Prof. J. Sebastian, University of Oviedo, Asturias, Spain, Prof. D. Perreault, Massachusetts Institute

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of Technology, Cambridge, Prof. J. C. Pedro, University of Aveiro, Aveiro, Portugal, and Dr. F. Raab, Green Mountain Radio Research Company, Colchester, VT. The contributions to this research line from previous members of the group, Dr. L. Cabria and L. Rizo, are also appreciated, as well as the support received from S. Pana, University of Cantabria, Santander, Spain, with die mounting and bonding, and from R. Baker, Cree Inc., Durham, NC, related to the GaN HEMT devices. Finally, the authors want to thank this TRANSACTIONS’ associate editor and reviewers for their kind comments and detailed suggestions to improve this paper’s manuscript. REFERENCES [1] E. McCune, “Envelope tracking or polar—Which is it?,” IEEE Microw. Mag., vol. 13, no. 4, pp. 34–56, May/Jun. 2012. [2] R. Foley, F. Waldron, J. Slowey, A. Alderman, B. Narveson, and S. C. O’Mathuna, “Technology roadmapping for power supply in package (PSiP) and power supply on chip (PwrSoC),” in 25th Annu. IEEE Appl. Power Electron. Conf. and Expo., Feb. 21–25, 2010, pp. 525–532. [3] M. K. Kazimierczuk and D. Czarkowski, Resonant Power Converters. Hoboken, NJ: Wiley, 2011. [4] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2nd ed. Berlin, Germany: Springer, 2001. [5] D. J. Perreault, H. Jingying, J. M. Rivas, H. Yehui, O. Leitermann, R. C. N. Pilawa-Podgurski, A. Sagneri, and C. R. Sullivan, “Opportunities and challenges in very high frequency power conversion,” in 24th Annu. IEEE Appl. Power Electron. Conf. and Expo., Mar. 2009, pp. 1–14. [6] T. M. Andersen, S. K. Christensen, A. Knott, and M. A. E. Andersen, “A VHF class E DC–DC converter with self-oscillating gate driver,” in 26th Annu. IEEE Appl. Power Electron. Conf. and Expo., Mar. 6–11, 2011, pp. 885–891. [7] J. M. Rivas, O. Leitermann, Y. Han, and D. J. Perreault, “A very high resonant inverter,” frequency DC–DC converter based on a class IEEE Trans. Power Electron., vol. 26, no. 10, pp. 2980–2992, Oct. 2011. [8] S. Djukic, D. Maksimovic, and Z. Popovic, “A planar 4.5-GHz DC–DC power converter,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 8, pp. 1457–1460, Aug. 1999. [9] F. C. Lee, “High-frequency quasi-resonant converter technologies,” Proc. IEEE, vol. 76, no. 4, pp. 377–390, Apr. 1988. [10] N. O. Sokal and A. D. Sokal, “Class E, a new class of high-efficiency tuned single-ended switching power amplifiers,” IEEE J. Solid-State Circuits, vol. SSC-10, no. 6, pp. 168–176, Jun. 1975. [11] R. J. Gutmann, “Application of RF circuit design principles to distributed power converters,” IEEE Trans. Ind. Electron. Control Instrum., vol. IECI-27, no. 3, pp. 156–164, Aug. 1980. [12] R. Redl, B. Molnár, and N. O. Sokal, “Class E resonant regulated DC/DC power converters: Analysis of operations, and experimental results at 1.5 MHz,” IEEE Trans. Power Electron., vol. PE-1, no. 2, pp. 111–120, Apr. 1986. [13] M. K. Kazimierczuk and J. Jozwik, “Resonant DC/DC converter with class-E inverter and class-E rectifier,” IEEE Trans. Ind. Electron., vol. 36, no. 4, pp. 468–478, Nov. 1989. [14] M. K. Kazimierczuk and J. Jozwik, “Class E narrowband resonant DC/DC converters,” IEEE Trans. Instrum. Meas., vol. 38, no. 6, pp. 1064–1068, Dec. 1989. [15] F. H. Raab, “Idealized operation of the class E tuned power amplifier,” IEEE Trans. Circuits Syst., vol. CS-24, no. 12, pp. 725–735, Dec. 1977. [16] D. C. Hamill, “Time reversal duality and the synthesis of a double class E DC–DC converter,” in 21st Power Electron. Specialist Conf., 1990, pp. 512–521. [17] A. Grebennikov and N. O. Sokal, Switchmode RF Power Amplifiers, 1st ed. New York: Elsevier, 2007. [18] M. K. Kazimierczuk, RF Power Amplifiers. New York: Wiley, 2008. [19] R. Beltran and F. H. Raab, “Lumped-element output networks for highefficiency power amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., Anaheim, CA, May 2010, pp. 324–327. [20] T. B. Mader and Z. B. Popović, “The transmission-line high-efficiency class-E amplifier,” IEEE Microw. Guided Wave Lett., vol. 5, no. 9, pp. 290–292, Sep. 1995.

[21] R. Marante, M. N. Ruiz, L. Rizo, L. Cabria, and J. A. Garcia, “A UHF class E DC/DC converter using GaN HEMTS,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [22] U. Gustavsson, T. Eriksson, H. M. Nemati, P. Saad, P. Singerl, and C. Fager, “An RF carrier bursting system using partial quantization noise cancellation,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 3, pp. 515–528, Mar. 2012. [23] H. Chireix, “High power outphasing modulation,” Proc. IRE, vol. 23, no. 11, pp. 1370–1392, Nov. 1935. [24] A. Birafane, M. El-Asmar, A. Kouki, B. Ammar, M. Helaoui, and F. M. Ghannouchi, “Analyzing LINC systems,” IEEE Microw. Mag., vol. 11, no. 5, pp. 59–71, Aug. 2010. [25] R. Beltran, F. H. Raab, and A. Velazquez, “HF outphasing transmitter using class-E power amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2009, pp. 757–760. [26] M. P. van der Heijden, M. Acar, J. S. Vromans, and D. A. Calvillo-Cortes, “A 19 W high-efficiency wideband CMOS-GAN class-E Chireix RF outphasing power amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2011, pp. 1–4. [27] W. H. Cantrell and W. A. Davis, “Amplitude modulator utilizing a high- class-E DC–DC converter,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, pp. 1721–1724. [28] F. H. Raab, “Intermodulation distortion in kahn-technique transmitters,” IEEE Trans. Microw. Theory Techn., vol. 44, no. 12, pp. 2273–2278, Dec. 1996. [29] J. C. Pedro, J. A. Garcia, and P. M. Cabral, “Nonlinear distortion analysis of polar transmitters,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 12, pp. 2757–2765, Dec. 2007. [30] P. Cabral, L. Cabria, F. Rodrigues, J. A. García, and J. C. Pedro, “Wireless transmitter capabilities through supply modulation,” Int. J. RF Microw. Comput.-Aided Eng., vol. 20, no. 2, pp. 241–251, Mar. 2010. [31] L. Cabria, J. A. Garcia, P. M. Cabral, and J. C. Pedro, “Linearization of a polar transmitter for EDGE applications,” in Int. Nonlinear Microw. Millim.-Wave Circuits Workshop, Nov. 24–25, 2008, pp. 115–118. [32] J. Hu, A. D. Sagneri, J. M. Rivas, Y. Han, S. M. Davis, and D. J. Perreault, “High-frequency resonant SEPIC converter with wide input and output voltage ranges,” IEEE Trans. Power Electron., vol. 27, no. 1, pp. 189–200, Jan. 2012. [33] J. S. Glaser and J. M. Rivas, “A 500 W push–pull DC–DC power converter with a 30 MHz switching frequency,” in 25th Annu. IEEE Appl. Power Electron. Conf. and Expo., Feb. 21–25, 2010, pp. 654–661. [34] N. Le Gallou, D. Sardin, C. Delepaut, M. Campovecchio, and S. Rochette, “Over 10 MHz bandwidth envelope-tracking DC/DC converter for flexible high power GaN amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 5–10, 2011, pp. 1–4. [35] V. Pala, H. Peng, P. Wright, M. M. Hella, and T. P. Chow, “Integrated high-frequency power converters based on GaAs pHEMT: Technology characterization and design examples,” IEEE Trans. Power Electron., vol. 27, no. 5, pp. 2644–2656, May 2012.

José A. García (S’98–A’00–M’02) received the Telecommunication Engineering degree (with honors) from the Instituto Superior Politécnico “José A. Echeverría” (ISPJAE), Havana, Cuba, in 1988, and the Ph.D. degree (with a University Prize) from the University of Cantabria, Santander, Spain, in 2000. From 1988 to 1991, he was a Radio System Engineer with a high-frequency (HF) communication center, where he designed antennas and HF circuits. From 1991 to 1995, he was an Instructor Professor with the Telecommunication Engineering Department, ISPJAE. From 1999 to 2000, he was with Thaumat Global Technology Systems, as a Radio Design Engineer involved with base-station arrays. From 2000 to 2001, he was a Microwave Design Engineer/Project Manager with TTI Norte, during which time he was in charge of the research line on SDR while involved with active antennas. From 2002 to 2005, he was a Senior Research Scientist with the University of Cantabria, where he is currently an Associate Professor. During 2011, he was a Visiting Researcher with the Microwave and RF Research Group, University of Colorado at Boulder. His main research interests include nonlinear characterization and modeling of active devices, as well as the design of power RF/microwave amplifiers, high-efficiency transmitting architectures (incorporating arrays), and RF dc/dc power converters. Dr. García has been a reviewer for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES.

GARCÍA et al.: GaN HEMT CLASS E RESONANT TOPOLOGIES FOR UHF DC/DC POWER CONVERSION

Reinel Marante Torres (S’12) was born in Havana, Cuba, on June 14, 1980. He received the B.S. degree in Telecommunication Engineering from the Instituto Superior Politécnico “José A. Echeverría” (ISPJAE), Havana, Cuba, in 2004, the Ms.C. degree from the University of Cantabria, Santander, Spain, in 2009, and is currently working toward the Ph.D. degree in Communication Engineering at the University of Cantabria. His research interests include active device nonlinear modeling and highly efficient transmission technologies.

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María de las Nieves Ruiz Lavín (S’12) was born in Santander, Spain, on September 19, 1983. She received the B.S. degree in Telecommunication Engineering from the University of Cantabria, Santander, Spain, in 2010, and is currently working toward the Ms.C degree at the Universidad del País Vasco, Bilbao, Spain Her research interests include high-efficiency microwave power amplifiers, rectifiers, oscillators, and converters.

Editor-in-Chief George E. Ponchak, Ph.D., FIEEE IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES Editorial Office c/o Mrs. Kim Tanger, Editorial Assistant Ohio Aerospace Institute 22800 Cedar Point Road Cleveland, Ohio 44142 E-mail: [email protected] or [email protected] Phone: 440-962-3023 Fax: 440-962-3057

Information for Authors The IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES is published monthly with a focus on that part of engineering and theory associated with microwave/millimeter-wave technology and components, electronic devices, guided wave structures and theory, electromagnetic theory, and Radio Frequency Hybrid and Monolithic Integrated Circuits, including mixed-signal circuits, from a few 100 MHz to THz. I. Paper Submission in Electronic Form Authors need to visit the website http://www.mtt.org/transactions/34-author-information-transactions.html for the author instructions. To reduce time from submission to publication of papers, the editorial office accepts manuscripts only in electronic form as .pdf files and all communications with authors will be via email. The files must not be larger than 1MB and no *.zip files are accepted. Submissions should be submitted through the ScholarOne Manuscripts site at: http://mc.manuscriptcentral.com/tmtt-ieee and use the templates provided under http://www.ieee.org/publications_standards/publications/authors/authors_journals.html (Template for all Transactions (except IEEE Transactions on Magnetics), two-column template; can also be requested from the editorial office). Figures, graphs and all other necessary information for reviewing the manuscript must be included in this file (as opposed to being attached to it as separate files) and placed at appropriate locations within the text rather than at the end: • • • • • • • • • •

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Digital Object Identifier 10.1109/TMTT.2012.2234366

Digital Object Identifier 10.1109/TMTT.2012.2234400

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2012 Index IEEE Transactions on Microwave Theory and Techniques Vol. 60 This index covers all technical items — papers, correspondence, reviews, etc. — that appeared in this periodical during 2012, and items from previous years that were commented upon or corrected in 2012. Departments and other items may also be covered if they have been judged to have archival value. The Author Index contains the primary entry for each item, listed under the first author’s name. The primary entry includes the coauthors’ names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination. The Subject Index contains entries describing the item under all appropriate subject headings, plus the first author’s name, the publication abbreviation, month, and year, and inclusive pages. Note that the item title is found only under the primary entry in the Author Index. AUTHOR INDEX A Aaen, P. H., see Zhang, L., TMTT March 2012 441-450 Aaen, P. H., Wood, J., Bridges, D., Zhang, L., Johnson, E., Pla, J. A., Barbieri, T., Snowden, C. M., Everett, J. P., and Kearney, M. J., Multiphysics Modeling of RF and Microwave High-Power Transistors; TMTT Dec. 2012 4013-4023 Aaron, T., see Trotta, S., TMTT March 2012 778-794 Abbosh, A. M., Design Method for Ultra-Wideband Bandpass Filter With Wide Stopband Using Parallel-Coupled Microstrip Lines; TMTT Jan. 2012 31-38 Abbosh, A. M., Compact Tunable Reflection Phase Shifters Using Short Section of Coupled Lines; TMTT Aug. 2012 2465-2472 Abdipour, A., see Kheirdoost, A., TMTT June 2012 1493-1499 Abdipour, A., see Honari, M. M., TMTT Nov. 2012 3633 Achar, R., see Saini, A. S., TMTT Nov. 2012 3359-3368 Adams, J., see Wu, J., TMTT June 2012 1587-1594 Adinolfi, V., see Voinigescu, S. P., TMTT Dec. 2012 4024-4034 Adnan, M., see Lee, W., TMTT Feb. 2012 370-380 Afsardoost, S., Eriksson, T., and Fager, C., Digital Predistortion Using a VectorSwitched Model; TMTT April 2012 1166-1174 Afshari, E., see Lee, W., TMTT Feb. 2012 370-380 Afshari, E., see Lee, W., TMTT Feb. 2012 329-339 Ahmed, O. S., Bakr, M. H., Li, X., and Nomura, T., A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters; TMTT Oct. 2012 2959-2971 Ahn, H.-R., and Nam, S., Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators; TMTT June 2012 1549-1559 Ahn, H.-R., Complex Impedance Transformers Consisting of Only Transmission-Line Sections; TMTT July 2012 2073-2084 Aihara, K., see Hirata, A., TMTT March 2012 881-895 Aja Abelan, B., Seelmann-Eggebert, M., Bruch, D., Leuther, A., Massler, H., Baldischweiler, B., Schlechtweg, M., Gallego-Puyol, J. D., Lopez-Fernandez, I., Diez-Gonzalez, C., Malo-Gomez, I., Villa, E., and Artal, E., 4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers; TMTT Dec. 2012 4080-4088 Akbarpour, M., Helaoui, M., and Ghannouchi, F. M., A Transformer-Less Load-Modulated (TLLM) Architecture for Efficient Wideband Power Amplifiers; TMTT Sept. 2012 2863-2874 Akmal, M., see Carrubba, V., TMTT June 2012 1928-1936 Alavi, M. S., Staszewski, R. B., de Vreede, L. C. N., Visweswaran, A., and Long, J. R., All-Digital RF Modulator; TMTT Nov. 2012 3513-3526 Alcaro, G., Visani, D., Tarlazzi, L., Faccin, P., and Tartarini, G., Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links; TMTT Jan. 2012 185-194 Alekseev, S. I., see Chahat, N., TMTT March 2012 827-832 Allender, C. J., see Rowe, D. J., TMTT June 2012 1699-1708 Alonso, J. I., see Pelaez-Perez, A. M., TMTT Oct. 2012 3126-3136 Aloui, S., see Yeh, H.-C., TMTT Dec. 2012 4066-4079 Alvandpour, A., see Landin, P. N., TMTT June 2012 1907-1915

Alvarez, J., Angulo, L., Rubio Bretones, A., and Garcia, S. G., A Spurious-Free Discontinuous Galerkin Time-Domain Method for the Accurate Modeling of Microwave Filters; TMTT Aug. 2012 2359-2369 Alvarez-Melcon, A., see Martinez-Mendoza, M., TMTT July 2012 2131-2141 Alvarez-Melcon, A., see Martinez-Mendoza, M., TMTT Nov. 2012 3369-3375 Amendola, G., see Boccia, L., TMTT July 2012 2287-2300 Amirkhizi, A. V., see Bayatpur, F., TMTT April 2012 1126-1135 Amjadi, M., and Jafari, E., Design of a Broadband Eight-Way Coaxial Waveguide Power Combiner; TMTT Jan. 2012 39-45 An, H.-W., see Kim, M.-G., TMTT Aug. 2012 2486-2493 An, K. H., see Yoon, Y., TMTT Jan. 2012 77-88 Anakabe, A., see Otegi, N., TMTT Dec. 2012 4145-4156 Analui, B., see Goel, A., TMTT May 2012 1375-1389 Andersson, C. M., Gustafsson, D., Yamanaka, K., Kuwata, E., Otsuka, H., Nakayama, M., Hirano, Y., Angelov, I., Fager, C., and Rorsman, N., Theory and Design of Class-J Power Amplifiers With Dynamic Load Modulation; TMTT Dec. 2012 3778-3786 Andersson, K., see Saad, P., TMTT June 2012 1840-1849 Andersson, K., see Thorsell, M., TMTT Jan. 2012 149-157 Andersson, M. A., Habibpour, O., Vukusic, J., and Stake, J., Resistive Graphene FET Subharmonic Mixers: Noise and Linearity Assessment; TMTT Dec. 2012 4035-4042 Ando, M., see Suga, R., TMTT March 2012 640-646 Angelov, I., see Andersson, C. M., TMTT Dec. 2012 3778-3786 Angulo, L., see Alvarez, J., TMTT Aug. 2012 2359-2369 Antonini, G., see Spina, D., TMTT Aug. 2012 2329-2338 Antonini, G., see Ferranti, F., TMTT March 2012 431-440 Antonsen, T., see Stantchev, G., TMTT April 2012 930-937 Antonsen, T. M., see Jabotinski, V., TMTT April 2012 915-929 Anza, S., Vicente, C., Gil, J., Mattes, M., Wolk, D., Wochner, U., Boria, V. E., Gimeno, B., and Raboso, D., Prediction of Multipactor Breakdown for Multicarrier Applications: The Quasi-Stationary Method; TMTT July 2012 2093-2105 Apaydin, N., Zhang, L., Sertel, K., and Volakis, J. L., Experimental Validation of Frozen Modes Guided on Printed Coupled Transmission Lines; TMTT June 2012 1513-1519 Apsel, A. B., see Xiang, B., TMTT Nov. 2012 3449-3457 Arana, V., see Umpierrez, P., TMTT Nov. 2012 3527-3541 Arasu, M. A., see Hou, D., TMTT Dec. 2012 3728-3738 Aref, A. F., and Negra, R., A Fully Integrated Adaptive Multiband Multimode Switching-Mode CMOS Power Amplifier; TMTT Aug. 2012 2549-2561 Arigong, B., see Shao, J., TMTT Aug. 2012 2410-2416 Arnedo, I., see Chudzik, M., TMTT Nov. 2012 3384-3394 Arnedo, I., Arregui, I., Lujambio, A., Chudzik, M., Laso, M. A. G., and Lopetegi, T., Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses; TMTT May 2012 1244-1257 Arregui, I., see Arnedo, I., TMTT May 2012 1244-1257 Arregui, I., see Chudzik, M., TMTT Nov. 2012 3384-3394 Arsenovic, A., see Chen, L., TMTT Sept. 2012 2894-2902 Artal, E., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Asbeck, P., see Kim, J., TMTT June 2012 1870-1877 Asbeck, P. M., see Hassan, M., TMTT May 2012 1321-1330 Asbeck, P. M., see Kwak, M., TMTT June 2012 1850-1861 Asbeck, P. M., see Presti, C. D., TMTT March 2012 604-618 Asoodeh, A., and Atarodi, M., A Full 360 Vector-Sum Phase Shifter With Very Low RMS Phase Error Over a Wide Bandwidth; TMTT June 2012 1626-1634 Atarodi, M., see Asoodeh, A., TMTT June 2012 1626-1634 Atesal, Y. A., see Cetinoneri, B., TMTT March 2012 692-701 Atia, A. E., see Lee, H.-M., TMTT May 2012 1266-1277 Attari, A. R., see Pourzadi, A., TMTT Nov. 2012 3395-3402 Aufinger, K., see Zhao, Y., TMTT Oct. 2012 3286-3299 Aufinger, K., see Pohl, N., TMTT March 2012 757-765 Azana, J., see Chudzik, M., TMTT Nov. 2012 3384-3394

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Bae, J., Cho, H., Song, K., Lee, H., and Yoo, H.-Y., The Signal Transmission Mechanism on the Surface of Human Body for Body Channel Communication; TMTT March 2012 582-593 Bae, J.-D., see Kang, B., TMTT July 2012 2178-2191 Bai, Y.-F., Wang, X.-H., Gao, C.-J., Huang, Q.-L., and Shi, X.-W., Design of Compact Quad-Frequency Impedance Transformer Using Two-Section Coupled Line; TMTT Aug. 2012 2417-2423 Bai, Z., see Sun, G., TMTT Sept. 2012 2723-2729 Baillargeat, D., see Perigaud, A., TMTT April 2012 965-974 Bakr, M. H., see Ahmed, O. S., TMTT Oct. 2012 2959-2971 Baldischweiler, B., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Balteanu, A., see Voinigescu, S. P., TMTT Dec. 2012 4024-4034 Balteanu, A., see Sarkas, I., TMTT March 2012 795-812 Balzano, Q., see Li, C.-H., TMTT July 2012 2267-2276 Bandler, J. W., see Dadash, M. S., TMTT Sept. 2012 2713-2722 Bao, M., see Kuylenstierna, D., TMTT Nov. 2012 3420-3430 Barbieri, T., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Barker, N. S., see Chen, L., TMTT Sept. 2012 2894-2902 Barker, N. S., see Chen, L., TMTT March 2012 647-654 Barroso, J. J., and Hasar, U. C., Comments on "A Unique Extraction of Metamaterial Parameters Based on Kramers-Kronig Relationship"; TMTT June 2012 1743-1744 Barrow, D. A., see Rowe, D. J., TMTT June 2012 1699-1708 Bassam, S. A., Kwan, A., Chen, W., Helaoui, M., and Ghannouchi, F. M., Subsampling Feedback Loop Applicable to Concurrent Dual-Band Linearization Architecture; TMTT June 2012 1990-1999 -Mode Dielectric Bastioli, S., and Snyder, R. V., Inline Pseudoelliptic Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Orthogonal Resonators; TMTT Dec. 2012 3988-4001 Bauwens, M., see Chen, L., TMTT Sept. 2012 2894-2902 Bayatpur, F., Amirkhizi, A. V., and Nemat-Nasser, S., Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies; TMTT April 2012 1126-1135 Beach, M. A., see Hone, T. M., TMTT June 2012 1797-1804 Beguhn, S., see Wu, J., TMTT Dec. 2012 3959-3968 Belenguer, A., Cascon, J., Borja, A. L., Esteban, H., and Boria, V. E., Dual Composite Right-/Left-Handed Coplanar Waveguide Transmission Line Using Inductively Connected Split-Ring Resonators; TMTT Oct. 2012 3035-3042 Belenguer, A., see Diaz Caballero, E., TMTT Feb. 2012 232-243 Belostotski, L., see Navaratne, D., TMTT Oct. 2012 3179-3188 Benech, P., see Quemerais, T., TMTT April 2012 1079-1085 Benedikt, J., see Carrubba, V., TMTT June 2012 1928-1936 Benedikt, J., see Hone, T. M., TMTT June 2012 1797-1804 Benito, D., see Chudzik, M., TMTT Nov. 2012 3384-3394 Bensmida, S., see Mimis, K., TMTT Aug. 2012 2562-2570 Bensmida, S., see Hone, T. M., TMTT June 2012 1797-1804 Berenguer, R., see Liu, J. Y.-C., TMTT May 2012 1342-1352 Beygi, A., see Roy, S., TMTT March 2012 451-463 Beygi, A., and Dounavis, A., An Instrumental Variable Vector-Fitting Approach for Noisy Frequency Responses; TMTT Sept. 2012 2702-2712 Bhan, V., see Xie, H., TMTT May 2012 1390-1396 Bila, S., see Perigaud, A., TMTT April 2012 965-974 Birafane, A., see El-Asmar, M., TMTT June 2012 1886-1895 Bird, T. S., see Wenzhi, W., TMTT Nov. 2012 3349-3358 Bjorsell, N., see Nader, C., TMTT Nov. 2012 3571-3581 Boccia, L., Russo, I., Amendola, G., and Di Massa, G., Multilayer AntennaFilter Antenna for Beam-Steering Transmit-Array Applications; TMTT July 2012 2287-2300 Bofill, A., see Trulls, X., TMTT Oct. 2012 3243-3253 Boppel, S., Lisauskas, A., Mundt, M., Seliuta, D., Minkevicius, L., Kasalynas, I., Valusis, G., Mittendorff, M., Winnerl, S., Krozer, V., and Roskos, H. G., CMOS Integrated Antenna-Coupled Field-Effect Transistors for the Detection of Radiation From 0.2 to 4.3 THz; TMTT Dec. 2012 3834-3843 Boria, E., see Diaz Caballero, E., TMTT Feb. 2012 232-243 Boria, V. E., see Anza, S., TMTT July 2012 2093-2105 Boria, V. E., see Cogollos, S., TMTT April 2012 1006-1017 Boria, V. E., see Belenguer, A., TMTT Oct. 2012 3035-3042 Borja, A. L., see Belenguer, A., TMTT Oct. 2012 3035-3042 Borngraber, J., see Mao, Y., TMTT Dec. 2012 3823-3833 Bosisio, R. G., see Xu, Y., TMTT Sept. 2012 2781-2790 + Check author entry for coauthors

Bostani, A., and Webb, J. P., Finite-Element Eigenvalue Analysis of Propagating and Evanescent Modes in 3-D Periodic Structures Using ModelOrder Reduction; TMTT Sept. 2012 2677-2683 Boumaiza, S., see Wu, D. Y.-T., TMTT Oct. 2012 3201-3213 Bovelli, S., see Ziegler, V., TMTT Dec. 2012 4209-4219 Brandao Faria, J. A., and Pires, M. P., Theory of Magnetic Transmission Lines; TMTT Oct. 2012 2941-2949 Brazil, T. J., see Tuffy, N., TMTT June 2012 1952-1963 Bridges, D., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Bruch, D., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Brumos, M., see Cogollos, S., TMTT April 2012 1006-1017 Bucholtz, F., see Diehl, J. F., TMTT Jan. 2012 195-200 Buckwalter, J. F., see Kim, J., TMTT June 2012 1870-1877 Buckwalter, J. F., see Kalantari, N., TMTT June 2012 1667-1675 Buckwalter, J. F., see Gupta, A. K., TMTT Oct. 2012 3272-3285 Buckwalter, J. F., see Gathman, T. D., TMTT Dec. 2012 3798-3809 Buckwalter, J. F., see Parlak, M., TMTT Dec. 2012 3810-3822 Buisman, K., see Huang, C., TMTT Dec. 2012 3699-3709 Bulja, S., and Grebennikov, A., Variable Reflection-Type Attenuators Based on Varactor Diodes; TMTT Dec. 2012 3719-3727 Burgos-Garcia, M., see de la Morena-Alvarez-Palencia, C., TMTT Aug. 2012 2634-2643

C Cai, W., see Chen, G., TMTT Feb. 2012 218-231 Cai, W., see Chen, G., TMTT June 2012 1745-1747 Calafiore, G. C., Chinea, A., and Grivet-Talocia, S., Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels; TMTT Oct. 2012 2990-3003 Caloz, C., see Zhang, Q., TMTT Aug. 2012 2394-2402 Caloz, C., see Gupta, S., TMTT Dec. 2012 3939-3949 Caloz, C., see Sounas, D. L., TMTT April 2012 901-914 Camacho-Penalosa, C., see Navarro-Tapia, M., TMTT April 2012 1146-1155 Camacho-Penalosa, C., see Esteban, J., TMTT Aug. 2012 2385-2393 Camarchia, V., see Rubio, J. M., TMTT Aug. 2012 2543-2548 Camblor, R., see Fernandez Garcia, M., TMTT Aug. 2012 2494-2504 Campovecchio, M., see Demenitroux, W., TMTT June 2012 1817-1828 Cangellaris, A. C., see Ochoa, J. S., TMTT Dec. 2012 3919-3926 Canos, A. J., see Penaranda-Foix, F. L., TMTT Sept. 2012 2730-2740 Cantu, H. I., Romeira, B., Kelly, A. E., Ironside, C. N., and Figueiredo, J. M. L., Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks; TMTT Sept. 2012 2903-2912 Cao, H., Nemati, H. M., Soltani Tehrani, A., Eriksson, T., and Fager, C., Digital Predistortion for High Efficiency Power Amplifier Architectures Using a Dual-Input Modeling Approach; TMTT Feb. 2012 361-369 Carroll, M. S., see Tombak, A., TMTT June 2012 1862-1869 Carrubba, V., Akmal, M., Quay, R., Lees, J., Benedikt, J., Cripps, S. C., and Tasker, P. J., The Continuous Inverse Class-F Mode With Resistive SecondHarmonic Impedance; TMTT June 2012 1928-1936 Casaletti, M., Sauleau, R., Ettorre, M., and Maci, S., Efficient Analysis of Metallic and Dielectric Posts in Parallel-Plate Waveguide Structures; TMTT Oct. 2012 2979-2989 Cascon, J., see Belenguer, A., TMTT Oct. 2012 3035-3042 Catala-Civera, J. M., see Penaranda-Foix, F. L., TMTT Sept. 2012 2730-2740 Caverly, R. H., Microwave and RF p-i-n Diode Model for Time-Domain Simulation; TMTT July 2012 2158-2164 Celi, D., see Voinigescu, S. P., TMTT Dec. 2012 4024-4034 Celuch, M., see Salski, B., TMTT Aug. 2012 2352-2358 Cetinoneri, B., Atesal, Y. A., Fung, A., and Rebeiz, G. M., -Band Amplifiers With 6-dB Noise Figure and Milliwatt-Level 170–200-GHz Doublers in 45-nm CMOS; TMTT March 2012 692-701 Chahat, N., Zhadobov, M., Sauleau, R., and Alekseev, S. I., New Method for Determining Dielectric Properties of Skin and Phantoms at Millimeter Waves Based on Heating Kinetics; TMTT March 2012 827-832 Chahat, N., Zhadobov, M., and Sauleau, R., Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves; TMTT July 2012 2259-2266 Chaker, M., see Mortazy, E., TMTT Feb. 2012 293-300 Chan, W. S., see Wong, Y. S., TMTT June 2012 1530-1539 Chang, C.-L., see Tseng, C.-H., TMTT July 2012 2085-2092 Chang, C.-L., see Tseng, C.-H., TMTT Oct. 2012 3151-3160 Chang, C.-Y., see Chang, W.-S., TMTT Nov. 2012 3376-3383

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Chang, C.-Y., see Lin, Y.-W., TMTT July 2012 2124-2130 Chang, C.-Y., see Kuo, Y.-T., TMTT Feb. 2012 250-260 Chang, H.-Y., and Chiu, Y.-T., -Band CMOS Differential and Quadrature Voltage-Controlled Oscillators for Low Phase-Noise and Low-Power Applications; TMTT Jan. 2012 46-59 Chang, H.-Y., see Yeh, Y.-L., TMTT June 2012 1617-1625 Chang, H.-Y., see Lin, C.-H., TMTT Oct. 2012 3232-3242 Chang, H.-Y., see Weng, S.-H., TMTT Nov. 2012 3458-3473 Chang, I.-C., see Kuo, J.-L., TMTT March 2012 743-756 Chang, M.-C. F., see Liu, J. Y.-C., TMTT May 2012 1342-1352 Chang, M.-C. F., see Gu, Q. J., TMTT May 2012 1365-1374 Chang, M.-C. F., see Tang, A., TMTT Dec. 2012 4129-4137 Chang, M.-C. F., see Jooyaie, A., TMTT Aug. 2012 2505-2511 Chang, S.-F., see Wei, M.-D., TMTT June 2012 1916-1927 Chang, W.-S., and Chang, C.-Y., A High Slow-Wave Factor Microstrip Structure With Simple Design Formulas and Its Application to Microwave Circuit Design; TMTT Nov. 2012 3376-3383 Chang, Y.-L., see Kuo, J.-L., TMTT March 2012 743-756 Chang, Y.-L., see Lu, H.-C., TMTT March 2012 766-777 Chang-Chien, P. P., see Leong, K. M. K. H., TMTT April 2012 998-1005 Chantre, A., see Dacquay, E., TMTT March 2012 813-826 Chappell, W. J., see Naglich, E. J., TMTT Jan. 2012 21-30 Chappell, W. J., see Liu, X., TMTT Feb. 2012 270-283 Chappell, W. J., see Naglich, E. J., TMTT May 2012 1258-1265 Chappell, W. J., see Lee, J., TMTT Aug. 2012 2424-2430 Chappell, W. J., see Huang, Y.-T., TMTT Sept. 2012 2886-2893 Chaudhary, G., Jeong, Y., and Lim, J., Harmonic Suppressed Dual-Band Bandpass Filters With Tunable Passbands; TMTT July 2012 2115-2123 Chavannes, N., see Li, C.-H., TMTT July 2012 2267-2276 Che, W., see Feng, W., TMTT June 2012 1560-1568 Chen, C., see Kong, C., TMTT Nov. 2012 3413-3419 Chen, C.-H., Huang, C.-H., Horng, T.-S., and Wu, S.-M., Highly Miniaturized Multiband Bandpass Filter Design Based on a Stacked Spiral Resonator Structure; TMTT May 2012 1278-1286 Chen, C.-T., see Hsiao, C.-H., TMTT June 2012 2000-2009 Chen, C.-T., Horng, T.-S., Peng, K.-C., and Li, C.-J., High-Gain and High-Efficiency EER/Polar Transmitters Using Injection-Locked Oscillators; TMTT Dec. 2012 4117-4128 Chen, D., Pan, W., Jiang, P., Jin, J., Mo, T., and Zhou, J., Reconfigurable DualChannel Multiband RF Receiver for GPS/Galileo/BD-2 Systems; TMTT Nov. 2012 3491-3501 Chen, G., Zhu, H., Cui, T., Chen, Z., Zeng, X., and Cai, W., Authors’ reply; TMTT June 2012 1745-1747 Chen, G., Zhu, H., Cui, T., Chen, Z., Zeng, X., and Cai, W., ParAFEMCap: A Parallel Adaptive Finite-Element Method for 3-D VLSI Interconnect Capacitance Extraction; TMTT Feb. 2012 218-231 Chen, H.-S., and Lu, L. H., An Open-Loop Half-Quadrature Hybrid for Multiphase Signals Generation; TMTT Jan. 2012 131-138 Chen, J., see Fu, S., TMTT March 2012 477-483 Chen, J., see Niknejad, A. M., TMTT June 2012 1784-1796 Chen, J., see Zong, Z.-Y., TMTT June 2012 1500-1512 Chen, J., see Hou, D., TMTT Dec. 2012 3728-3738 Chen, J.-H., Helmi, S. R., Pajouhi, H., Sim, Y., and Mohammadi, S., A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN; TMTT Dec. 2012 4089-4096 Chen, J.-T., see Lee, J.-W., TMTT Dec. 2012 3642-3655 Chen, J.-X., see Zhu, F., TMTT Oct. 2012 3062-3070 Chen, K., Liu, X., and Peroulis, D., Widely Tunable High-Efficiency Power Amplifier With Ultra-Narrow Instantaneous Bandwidth; TMTT Dec. 2012 3787-3797 Chen, K., and Peroulis, D., Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation; TMTT June 2012 1829-1839 Chen, K., and Peroulis, D., Design of Broadband Highly Efficient HarmonicF Mode Tuned Power Amplifier Using In-Band Continuous Class-F Transferring; TMTT Dec. 2012 4107-4116 Chen, K.-H., see Liu, S.-L., TMTT July 2012 2165-2177 Chen, L., Loschonsky, M., and Reindl, L. M., Autoregressive Modeling of Mobile Radio Propagation Channel in Building Ruins; TMTT May 2012 1478-1489 Chen, L., Wood, J., Raman, S., and Barker, N. S., Vertical RF Transition With Mechanical Fit for 3-D Heterogeneous Integration; TMTT March 2012 647-654

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4235

Chen, L., Zhang, C., Reck, T. J., Arsenovic, A., Bauwens, M., Groppi, C., Lichtenberger, A. W., Weikle, R. M., and Barker, N. S., Terahertz Micromachined On-Wafer Probes: Repeatability and Reliability; TMTT Sept. 2012 2894-2902 Chen, M. Y., Pham, D., Subbaraman, H., Lu, X., and Chen, R. T., Conformal Ink-Jet Printed -Band Phased-Array Antenna Incorporating Carbon Nanotube Field-Effect Transistor Based Reconfigurable True-Time Delay Lines; TMTT Jan. 2012 179-184 Chen, P., see Gong, K., TMTT Oct. 2012 3071-3078 Chen, R. T., see Chen, M. Y., TMTT Jan. 2012 179-184 Chen, S., and Xue, Q, Optimized Load Modulation Network for Doherty Power Amplifier Performance Enhancement; TMTT Nov. 2012 3474-3481 Chen, T., Dubuc, D., Poupot, M., Fournie, J.-J., and Grenier, K., Accurate Nanoliter Liquid Characterization Up to 40 GHz for Biomedical Applications: Toward Noninvasive Living Cells Monitoring; TMTT Dec. 2012 4171-4177 Chen, W., see Liu, Y.-J., TMTT Nov. 2012 3559-3570 Chen, W., see Bassam, S. A., TMTT June 2012 1990-1999 Chen, X., see Kong, C., TMTT Nov. 2012 3413-3419 Chen, X.-P., see He, F. F., TMTT April 2012 1156-1165 Chen, Y.-C., see Huang, C.-C., TMTT Dec. 2012 4138-4144 Chen, Y.-T., Li, M.-W., Kuo, H.-C., Huang, T.-H., and Chuang, H.-R., LowVoltage -Band Divide-by-3 Injection-Locked Frequency Divider With Floating-Source Differential Injector; TMTT Jan. 2012 60-67 Chen, Z., see Chen, G., TMTT Feb. 2012 218-231 Chen, Z., see Wang, C.-C., TMTT May 2012 1307-1320 Chen, Z., see Chen, G., TMTT June 2012 1745-1747 Cheng, C.-C., and Rebeiz, G. M., A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control; TMTT Aug. 2012 2431-2438 Cheng, J.-C., see Shie, C.-I., TMTT March 2012 471-476 Cheng, K.-K. M., and Yeung, S., A Novel Dual-Band 3-dB Branch-Line Coupler Design With Controllable Bandwidths; TMTT Oct. 2012 3055-3061 Cheng, S., see Tripodi, L., TMTT Dec. 2012 3761-3768 Cheng, S.-J., see Diao, S., TMTT Jan. 2012 120-130 Chernin, D., see Stantchev, G., TMTT April 2012 930-937 Chernin, D., see Jabotinski, V., TMTT April 2012 915-929 Chevalier, P., see Dacquay, E., TMTT March 2012 813-826 Chevalier, P., see Voinigescu, S. P., TMTT Dec. 2012 4024-4034 Chiang, M.-C., see Yang, C.-L., TMTT April 2012 989-997 Chiang, Y.-C., see Yang, C.-L., TMTT April 2012 989-997 Chiang, Y.-C., see Shie, C.-I., TMTT March 2012 471-476 Chin, A., see Liu, S.-L., TMTT July 2012 2165-2177 Chinea, A., see Calafiore, G. C., TMTT Oct. 2012 2990-3003 Chiong, C.-C., see Yeh, H.-C., TMTT Dec. 2012 4066-4079 Chiong, C.-C., see Weng, S.-H., TMTT Nov. 2012 3458-3473 Chiou, Y.-C., and Rebeiz, G. M., A Quasi Elliptic Function 1.75–2.25 GHz 3-Pole Bandpass Filter With Bandwidth Control; TMTT Feb. 2012 244-249 Chisum, J. D., and Popovic, Z., Performance Limitations and Measurement Analysis of a Near-Field Microwave Microscope for Nondestructive and Subsurface Detection; TMTT Aug. 2012 2605-2615 Chiu, H.-C., see Yang, C.-L., TMTT April 2012 989-997 Chiu, Y.-T., see Chang, H.-Y., TMTT Jan. 2012 46-59 Cho, H., see Bae, J., TMTT March 2012 582-593 Cho, S., see Kim, J., TMTT Oct. 2012 3254-3262 Cho, Y.-H., see Wang, X.-G., TMTT June 2012 1569-1576 Choi, J. H., see Sun, J. S., TMTT Dec. 2012 3950-3958 Choi, S., see Ozkeskin, F. M., TMTT June 2012 1595-1604 Chou, S.-C., see Shie, C.-I., TMTT March 2012 471-476 Chou, W.-H., see Li, W.-T., TMTT Aug. 2012 2512-2523 Chowdhury, D., see Niknejad, A. M., TMTT June 2012 1784-1796 Christou, M. A., see Polycarpou, A. C., TMTT Oct. 2012 2950-2958 Chu, L.-W., see Lin, C.-Y., TMTT March 2012 714-723 Chu, Q.-X., see Lin, F., TMTT May 2012 1226-1234 Chu, Q.-X., see Lin, F., TMTT Sept. 2012 2935-2936 Chuang, H.-R., see Li, M.-W., TMTT March 2012 679-685 Chuang, H.-R., see Chen, Y.-T., TMTT Jan. 2012 60-67 Chudzik, M., see Arnedo, I., TMTT May 2012 1244-1257 Chudzik, M., Arnedo, I., Lujambio, A., Arregui, I., Gardeta, I., Teberio, F., Azana, J., Benito, D., Laso, M. A. G., and Lopetegi, T., Design of Transmission-Type th-Order Differentiators in Planar Microwave Technology; TMTT Nov. 2012 3384-3394 Chung, S.-J., see Lin, T.-W., TMTT Sept. 2012 2808-2814 Clive Tzuang, C.-K., see Hsieh, K.-A., TMTT June 2012 1649-1657

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Coen, C., see Donado Morcillo, C. A., TMTT Dec. 2012 3856-3867 Cogollos, S., Brumos, M., Boria, V. E., Vicente, C., Gil, J., Gimeno, B., and Guglielmi, M., A Systematic Design Procedure of Classical Dual-Mode Circular Waveguide Filters Using an Equivalent Distributed Model; TMTT April 2012 1006-1017 Colantonio, P., see Saad, P., TMTT June 2012 1840-1849 Collado, A., see Kim, S., TMTT Dec. 2012 4178-4186 Collantes, J.-M., see Otegi, N., TMTT Dec. 2012 4145-4156 Collantes, J.-M., see Narendra, K., TMTT Oct. 2012 3189-3200 Corona-Chavez, A., see Sun, J. S., TMTT Dec. 2012 3950-3958 Correra, F. S., see Serrano, A. L. C., TMTT March 2012 484-493 Costa, J., see Tombak, A., TMTT June 2012 1862-1869 Cressler, J. D., see Donado Morcillo, C. A., TMTT Dec. 2012 3856-3867 Cripps, S. C., see Carrubba, V., TMTT June 2012 1928-1936 Cross, A. W., see Zhang, L., TMTT Jan. 2012 1-7 Crovetti, P. S., Reproduction of the Effects of an Arbitrary Radiated Field by Ground Current Injection; TMTT April 2012 1136-1145 Cruciani, S., see Feliziani, M., TMTT Dec. 2012 3656-3666 Cui, T., see Chen, G., TMTT June 2012 1745-1747 Cui, T., see Chen, G., TMTT Feb. 2012 218-231

D

Dabag, H., see Kim, J., TMTT June 2012 1870-1877 Dacquay, E., Tomkins, A., Yau, K. H. K., Laskin, E., Chevalier, P., Chantre, A., Sautreuil, B., and Voinigescu, S. P., -Band Total Power Radiometer Performance Optimization in an SiGe HBT Technology; TMTT March 2012 813-826 Dacquay, E., see Voinigescu, S. P., TMTT Dec. 2012 4024-4034 Dadash, M. S., Nikolova, N. K., and Bandler, J. W., Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures; TMTT Sept. 2012 2713-2722 Dahlberg, K., see Silvonen, K., TMTT Nov. 2012 3551-3558 Dai, G.-L., Wei, X.-C., Li, E.-P., and Xia, M.-Y., Novel Dual-Band Out-ofPhase Power Divider With High Power-Handling Capability; TMTT Aug. 2012 2403-2409 Dai, L.-C., see Deng, P.-H., TMTT June 2012 1520-1529 Dani, A., Roberg, M., and Popovic, Z., PA Efficiency and Linearity Enhancement Using External Harmonic Injection; TMTT Dec. 2012 4097-4106 Darraji, R., Ghannouchi, F. M., and Helaoui, M., Mitigation of Bandwidth Limitation in Wireless Doherty Amplifiers With Substantial Bandwidth Enhancement Using Digital Techniques; TMTT Sept. 2012 2875-2885 Darwish, A. M., Hung, H. A., and Ibrahim, A. A., AlGaN/GaN HEMT With Distributed Gate for Channel Temperature Reduction; TMTT April 2012 1038-1043 Day, P. K., see Noroozian, O., TMTT May 2012 1235-1243 de Cos, J., Suarez, A., and Ramirez, F., Analysis of Oscillation Modes in FreeRunning Ring Oscillators; TMTT Oct. 2012 3137-3150 De Donno, D., Esposito, A., Monti, G., and Tarricone, L., MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit; TMTT Sept. 2012 2693-2701 de la Morena-Alvarez-Palencia, C., Mabrouk, K., Huyart, B., Mbaye, A., and Burgos-Garcia, M., Direct Baseband I-Q Regeneration Method for FivePort Receivers Improving DC-Offset and Second-Order Intermodulation Distortion Rejection; TMTT Aug. 2012 2634-2643 De La Torre Medina, J., see Hamoir, G., TMTT July 2012 2152-2157 de Langen, M., see Nazarian, A. L., TMTT Dec. 2012 3683-3692 de las Nieves Ruiz Lavin, M., see Garcia, J. A., TMTT Dec. 2012 4220-4229 De Santis, V., Ear Temperature Increase Produced by Cellular Phones Under Extreme Exposure Conditions; TMTT June 2012 1728-1734 de Vreede, L. C. N., see Huang, C., TMTT Dec. 2012 3699-3709 de Vreede, L. C. N., see Alavi, M. S., TMTT Nov. 2012 3513-3526 Deal, W. R., see Leong, K. M. K. H., TMTT April 2012 998-1005 Deal, W. R., see Radisic, V., TMTT March 2012 724-729 Dehlink, B., see Trotta, S., TMTT March 2012 778-794 Delgado-Restituto, M., see Masuch, J., TMTT May 2012 1413-1423 Dellier, S., see Demenitroux, W., TMTT June 2012 1817-1828 Demenitroux, W., Maziere, C., Gatard, E., Dellier, S., Campovecchio, M., and Quere, R., Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers; TMTT June 2012 1817-1828 Deng, K., see Sun, S.-J., TMTT Dec. 2012 3667-3673 + Check author entry for coauthors

Deng, P.-H., and Dai, L.-C., Unequal Wilkinson Power Dividers With Favorable Selectivity and High-Isolation Using Coupled-Line Filter Transformers; TMTT June 2012 1520-1529 Dening, D. C., see Tombak, A., TMTT June 2012 1862-1869 Deslandes, D., see Djerafi, T., TMTT Aug. 2012 2448-2455 Devgan, P. S., see Diehl, J. F., TMTT Jan. 2012 195-200 Dhaene, T., see Ferranti, F., TMTT March 2012 431-440 Dhaene, T., see Spina, D., TMTT Aug. 2012 2329-2338 Di Massa, G., see Boccia, L., TMTT July 2012 2287-2300 Dian, B. C., see Huang, Y.-T., TMTT Sept. 2012 2886-2893 Diao, S., Zheng, Y., Gao, Y., Cheng, S.-J., Yuan, X., Je, M., and Heng, C.-H., A 50-Mb/s CMOS QPSK/O-QPSK Transmitter Employing Injection Locking for Direct Modulation; TMTT Jan. 2012 120-130 Diaz Caballero, E., Esteban, H., Belenguer, A., and Boria, E., Efficient Analysis of Substrate Integrated Waveguide Devices Using Hybrid Mode Matching Between Cylindrical and Guided Modes; TMTT Feb. 2012 232-243 Dickhoff, R., see Jacob, M., TMTT March 2012 833-844 Diehl, J. F., Urick, V. J., McDermitt, C. S., Bucholtz, F., Devgan, P. S., and Williams, K. J., The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration; TMTT Jan. 2012 195-200 Diez-Gonzalez, C., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Ding, M., Gard, K. G., and Steer, M. B., A Highly Linear and Efficient CMOS RF Power Amplifier With a 2-D Circuit Synthesis Technique; TMTT Sept. 2012 2851-2862 Ding, P.-P., Qiu, C.-W., Zouhdi, S., and Yeo, S. P., Rigorous Derivation and Fast Solution of Spatial-Domain Green’s Functions for Uniaxial Anisotropic Multilayers Using Modified Fast Hankel Transform Method; TMTT Feb. 2012 205-217 Dixon, J., see Trotta, S., TMTT March 2012 778-794 Djerafi, T., Wu, K., and Deslandes, D., A Temperature-Compensation Technique for Substrate Integrated Waveguide Cavities and Filters; TMTT Aug. 2012 2448-2455 Donado Morcillo, C. A., Patterson, C. E., Lacroix, B., Coen, C., Poh, C. H. J., Cressler, J. D., and Papapolymerou, J., An Ultra-Thin, High-Power, and Multilayer Organic Antenna Array With T/R Functionality in the -Band; TMTT Dec. 2012 3856-3867 Donaldson, C. R., see Zhang, L., TMTT Jan. 2012 1-7 Dong, Y., see Wu, C.-T. M., TMTT April 2012 1027-1037 Douglas, M., see Li, C.-H., TMTT July 2012 2267-2276 Dounavis, A., see Beygi, A., TMTT Sept. 2012 2702-2712 Dounavis, A., see Roy, S., TMTT March 2012 451-463 Dubuc, D., see Chen, T., TMTT Dec. 2012 4171-4177 Duran-Sindreu, M., see Naqui, J., TMTT Oct. 2012 3023-3034

E Eberspacher, M. A., and Eibert, T. F., Analysis of Composite Right/LeftHanded Unit Cells Based on Even–Odd-Mode Excitation; TMTT May 2012 1186-1196 Eccleston, K. W., Mode Analysis of the Corrugated Substrate Integrated Waveguide; TMTT Oct. 2012 3004-3012 Ederra, I., see Liberal, I., TMTT Sept. 2012 2752-2759 Ederra, I., see Liberal, I., TMTT July 2012 2055-2065 Ehrig, M., see Ziegler, V., TMTT Dec. 2012 4209-4219 Eibert, T. F., see Eberspacher, M. A., TMTT May 2012 1186-1196 Eibert, T. F., see Kilic, E., TMTT May 2012 1437-1443 Eickhoff, R., see Mayer, U., TMTT March 2012 567-573 El-Asmar, M., Birafane, A., Helaoui, M., Kouki, A. B., and Ghannouchi, F. M., Analytical Design Methodology of Outphasing Amplification Systems Using a New Simplified Chireix Combiner Model; TMTT June 2012 18861895 Eleftheriades, G.V., see Memarian, M., TMTT Dec. 2012 3893-3907 Ellinger, F., see Fritsche, D., TMTT Oct. 2012 3223-3231 Ellinger, F., see Wickert, M., TMTT April 2012 1097-1104 Ellinger, F., see Mayer, U., TMTT March 2012 567-573 Elmadjian, R. N., see Leong, K. M. K. H., TMTT April 2012 998-1005 Entesari, K., see Sekar, V., TMTT May 2012 1444-1455 Entesari, K., see Helmy, A. A., TMTT Dec. 2012 4157-4170 Eom, B. H., see Noroozian, O., TMTT May 2012 1235-1243 Erguvan, D., see Wei, M.-D., TMTT June 2012 1916-1927 Eriksson, T., see Afsardoost, S., TMTT April 2012 1166-1174

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Eriksson, T., see Cao, H., TMTT Feb. 2012 361-369 Erni, D., see Meng, F.-Y., TMTT Oct. 2012 3013-3022 Ernst, C., see Martinez-Mendoza, M., TMTT Nov. 2012 3369-3375 Ernst, C., see Martinez-Mendoza, M., TMTT July 2012 2131-2141 Escotte, L., see Gonneau, E., TMTT Aug. 2012 2616-2621 Esposito, A., see De Donno, D., TMTT Sept. 2012 2693-2701 Essen, H., see Hantscher, S., TMTT March 2012 870-880 Esteban, H., see Diaz Caballero, E., TMTT Feb. 2012 232-243 Esteban, H., see Belenguer, A., TMTT Oct. 2012 3035-3042 Esteban, J., Camacho-Penalosa, C., Page, J. E., and Martin-Guerrero, T. M., Generalized Lattice Network-Based Balanced Composite Right-/Left-Handed Transmission Lines; TMTT Aug. 2012 2385-2393 Esteban, J., see Navarro-Tapia, M., TMTT April 2012 1146-1155 Esteban, J., see Varela, J. E., TMTT March 2012 419-430 Ettorre, M., see Casaletti, M., TMTT Oct. 2012 2979-2989 Everett, J. P., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Evseev, S. B., Nanver, L. K., and Milosaviljevic, S., Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates; TMTT Nov. 2012 3542-3550

Florian, C., Paganelli, R. P., and Lonac, J. A., 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules; TMTT June 2012 1805-1816 Fournie, J.-J., see Chen, T., TMTT Dec. 2012 4171-4177 Fournier, J.-M., see Quemerais, T., TMTT April 2012 1079-1085 Francois, B., and Reynaert, P., A Fully Integrated Watt-Level Linear 900-MHz CMOS RF Power Amplifier for LTE-Applications; TMTT June 2012 18781885 Fritsche, D., Wolf, R., and Ellinger, F., Analysis and Design of a Stacked Power Amplifier With Very High Bandwidth; TMTT Oct. 2012 3223-3231 Fritzin, J., see Landin, P. N., TMTT June 2012 1907-1915 Frolik, J. L., see Nassar, I. T., TMTT Oct. 2012 3309-3316 Fu, S., Wu, B., Chen, J., Sun, S., and Liang, C., Novel Second-Order Dual-Mode Dual-Band Filters Using Capacitance Loaded Square Loop Resonator; TMTT March 2012 477-483 Fu, Z., see Xiang, B., TMTT Nov. 2012 3449-3457 Fung, A., see Cetinoneri, B., TMTT March 2012 692-701 Fusco, V., see Zelenchuk, D. E., TMTT Oct. 2012 3300-3308 Fusco, V. F., see Thian, M., TMTT March 2012 655-659

F

G

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Gaebler, A., see Karabey, O. H., TMTT May 2012 1297-1306 Gallacher, T. F., Sondena, R., Robertson, D. A., and Smith, G. M., Optical Modulation of Millimeter-Wave Beams Using a Semiconductor Substrate; TMTT July 2012 2301-2309 Gallego-Puyol, J. D., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Gao, C.-J., see Bai, Y.-F., TMTT Aug. 2012 2417-2423 Gao, X., see Gu, S., TMTT Dec. 2012 3877-3885 Gao, Y., see Diao, S., TMTT Jan. 2012 120-130 Garcia, J. A., Marante, R., and de las Nieves Ruiz Lavin, M., GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion; TMTT Dec. 2012 4220-4229 Garcia, S. G., see Alvarez, J., TMTT Aug. 2012 2359-2369 Garcia-Vigueras, M., see Rodriguez-Berral, R., TMTT March 2012 405-418 Gard, K. G., see Ding, M., TMTT Sept. 2012 2851-2862 Gardeta, I., see Chudzik, M., TMTT Nov. 2012 3384-3394 Garelli, M., and Ferrero, A., A Unified Theory for -Parameter Uncertainty Evaluation; TMTT Dec. 2012 3844-3855 Gatard, E., see Demenitroux, W., TMTT June 2012 1817-1828 Gathman, T. D., and Buckwalter, J. F., An 8-bit Integrate-and-Sample Receiver for Rate-Scalable Photonic Analog-to-Digital Conversion; TMTT Dec. 2012 3798-3809 Gea, S.-B., see Li, W.-T., TMTT Aug. 2012 2512-2523 Gedney, S. D., see Zhao, B., TMTT Sept. 2012 2684-2692 Geng, Y., see Sun, J., TMTT Sept. 2012 2815-2822 Georgiadis, A., see Kim, S., TMTT Dec. 2012 4178-4186 Ghadiri, A., and Moez, K., High-Quality-Factor Active Capacitors for Millimeter-Wave Applications; TMTT Dec. 2012 3710-3718 Ghannouchi, F. M., see Akbarpour, M., TMTT Sept. 2012 2863-2874 Ghannouchi, F. M., see Darraji, R., TMTT Sept. 2012 2875-2885 Ghannouchi, F. M., see Bassam, S. A., TMTT June 2012 1990-1999 Ghannouchi, F. M., see El-Asmar, M., TMTT June 2012 1886-1895 Ghannouchi, F. M., see Liu, Y.-J., TMTT Nov. 2012 3559-3570 Gharibdoust, K., Mousavi, N., Kalantari, M., Moezzi, M., and Medi, A., A Fully Integrated 0.18- m CMOS Transceiver Chip for -Band PhasedArray Systems; TMTT July 2012 2192-2202 Ghazinour, A., see Trotta, S., TMTT March 2012 778-794 Ghione, G., see Rubio, J. M., TMTT Aug. 2012 2543-2548 Giammello, V., Ragonese, E., and Palmisano, G., A Transformer-Coupling Current-Reuse SiGe HBT Power Amplifier for 77-GHz Automotive Radar; TMTT June 2012 1676-1683 Gianchandani, Y. B., see Ozkeskin, F. M., TMTT June 2012 1595-1604 Giannini, F., see Saad, P., TMTT June 2012 1840-1849 Gil, J., see Cogollos, S., TMTT April 2012 1006-1017 Gil, J., see Anza, S., TMTT July 2012 2093-2105 Gimeno, B., see Anza, S., TMTT July 2012 2093-2105 Gimeno, B., see Cogollos, S., TMTT April 2012 1006-1017 Girbau, D., Ramos, (FixMe)., Lazaro, A., Rima, S., and Villarino, R., Passive Wireless Temperature Sensor Based on Time-Coded UWB Chipless RFID Tags; TMTT Nov. 2012 3623-3632 Glisic, S., see Ziegler, V., TMTT Dec. 2012 4209-4219

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Goel, A., Analui, B., and Hashemi, H., A 130-nm CMOS 100-Hz–6-GHz Reconfigurable Vector Signal Analyzer and Software-Defined Receiver; TMTT May 2012 1375-1389 Goh, W. L., see Hou, D., TMTT Dec. 2012 3728-3738 Gomez-Polo, C., see Liberal, I., TMTT July 2012 2055-2065 Gong, K., Hong, W., Zhang, Y., Chen, P., and You, C. J., Substrate Integrated Waveguide Quasi-Elliptic Filters With Controllable Electric and Magnetic Mixed Coupling; TMTT Oct. 2012 3071-3078 Gong, Z., see Lin, F., TMTT May 2012 1226-1234 Gonneau, E., and Escotte, L., Low-Frequency Noise Sources and Gain Stability in Microwave Amplifiers for Radiometry; TMTT Aug. 2012 2616-2621 Gonzalo, R., see Liberal, I., TMTT July 2012 2055-2065 Gonzalo, R., see Liberal, I., TMTT Sept. 2012 2752-2759 Gorospe, B. S., see Leong, K. M. K. H., TMTT April 2012 998-1005 Gotzen, R., see Tripodi, L., TMTT Dec. 2012 3761-3768 Goussetis, G., see Zelenchuk, D. E., TMTT Oct. 2012 3300-3308 Grass, E., see Ziegler, V., TMTT Dec. 2012 4209-4219 Grebennikov, A., see Bulja, S., TMTT Dec. 2012 3719-3727 Grebennikov, A., and Wong, J., A Dual-Band Parallel Doherty Power Amplifier for Wireless Applications; TMTT Oct. 2012 3214-3222 Grenier, K., see Chen, T., TMTT Dec. 2012 4171-4177 Grichener, A., and Rebeiz, G. M., A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies; TMTT Aug. 2012 2622-2633 Grivet-Talocia, S., see Calafiore, G. C., TMTT Oct. 2012 2990-3003 Groppi, C., see Chen, L., TMTT Sept. 2012 2894-2902 Gruszczynski, S., see Wincza, K., TMTT May 2012 1218-1225 Gu, Q. J., Xu, Z., and Chang, M.-C. F., Two-Way Current-Combining -Band Power Amplifier in 65-nm CMOS; TMTT May 2012 1365-1374 Gu, S., Li, C., Gao, X., Sun, Z., and Fang, G., Terahertz Aperture Synthesized Imaging With Fan-Beam Scanning for Personnel Screening; TMTT Dec. 2012 3877-3885 Guan, L., see Yu, C., TMTT Dec. 2012 4198-4208 Guan, L., see Tuffy, N., TMTT June 2012 1952-1963 Guan, L., and Zhu, A., Optimized Low-Complexity Implementation of Least Squares Based Model Extraction for Digital Predistortion of RF Power Amplifiers; TMTT March 2012 594-603 Guerrieri, J. R., see Kuester, D. G., TMTT July 2012 2248-2258 Guglielmi, M., see Cogollos, S., TMTT April 2012 1006-1017 Guinvarc’h, R., see Fang, H. R., TMTT Nov. 2012 3440-3448 Guo, Y. J., see Wenzhi, W., TMTT Nov. 2012 3349-3358 Guo, Y.-X., see Long, Y., TMTT Oct. 2012 3088-3095 Gupta, A. K., and Buckwalter, J. F., Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators; TMTT Oct. 2012 32723285 Gupta, S., Sounas, D. L., Nguyen, H. V., Zhang, Q., and Caloz, C., CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution; TMTT Dec. 2012 3939-3949 Gupta, S., see Zhang, Q., TMTT Aug. 2012 2394-2402 Gustafsson, D., see Andersson, C. M., TMTT Dec. 2012 3778-3786 Gustat, H., see Ostrovskyy, P., TMTT Aug. 2012 2524-2531 Guyette, A. C., Intrinsically Switched Varactor-Tuned Filters and Filter Banks; TMTT April 2012 1044-1056 H Ha, J., Lee, S., Min, B.-W., and Lee, Y., Application of Stepped-Impedance Technique for Bandwidth Control of Dual-Band Filters; TMTT July 2012 2106-2114 Habibpour, O., see Andersson, M. A., TMTT Dec. 2012 4035-4042 Haddadi, K., and Lasri, T., Formulation for Complete and Accurate Calibration of Six-Port Reflectometer; TMTT March 2012 574-581 Hagelen, M., see Hantscher, S., TMTT March 2012 870-880 Hamoir, G., De La Torre Medina, J., Piraux, L., and Huynen, I., Self-Biased Nonreciprocal Microstrip Phase Shifter on Magnetic Nanowired Substrate Suitable for Gyrator Applications; TMTT July 2012 2152-2157 Hampel, S. K., Schmitz, O., Tiebout, M., Mertens, K., and Rolfes, I., 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications; TMTT April 2012 1105-1116 Han, L., see He, F. F., TMTT April 2012 1156-1165 Han, L., and Wu, K., 24-GHz Integrated Radio and Radar System Capable of Time-Agile Wireless Communication and Sensing; TMTT March 2012 619-631 + Check author entry for coauthors

Handel, P., see Nader, C., TMTT Nov. 2012 3571-3581 Handel, P., see Landin, P. N., TMTT Nov. 2012 3582-3590 Hantscher, S., Schlenther, B., Hagelen, M., Lang, S. A., Essen, H., Tessmann, A., Hulsmann, A., Leuther, P., and Schlechtweg, M., Security Pre-screening of Moving Persons Using a Rotating Multichannel -Band Radar; TMTT March 2012 870-880 Hasan, A., and Helaoui, M., Novel Modeling and Calibration Approach for Multiport Receivers Mitigating System Imperfections and Hardware Impairments; TMTT Aug. 2012 2644-2653 Hasan, S. M. R., see Li, J., TMTT Oct. 2012 3120-3125 Hasar, U. C., see Barroso, J. J., TMTT June 2012 1743-1744 Hasch, J., see Sarkas, I., TMTT March 2012 795-812 Hasch, J., Topak, E., Schnabel, R., Zwick, T., Weigel, R., and Waldschmidt, C., Millimeter-Wave Technology for Automotive Radar Sensors in the 77 GHz Frequency Band; TMTT March 2012 845-860 Hashemi, H., see Goel, A., TMTT May 2012 1375-1389 Hashemi, H., see Imani, A., TMTT Dec. 2012 3749-3760 Hashemi, H., see Safarian, Z., TMTT Dec. 2012 4053-4065 Hassan, M., Larson, L. E., Leung, V. W., Kimball, D. F., and Asbeck, P. M., A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications; TMTT May 2012 1321-1330 Hatefi Ardakani, H., Fallahzadeh, S., and Rashed-Mohassel, J., Phase Velocities Equalization of Coupled Microstrip Lines Using -Shaped Particles and Suppression of the Second Harmonic; TMTT March 2012 464-470 Hauck, T., see Trotta, S., TMTT March 2012 778-794 He, F. F., Wu, K., Hong, W., Han, L., and Chen, X.-P., Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology; TMTT April 2012 1156-1165 He, J., Xiong, Y.-Z., and Zhang, Y. P., Analysis and Design of 60-GHz SPDT Switch in 130-nm CMOS; TMTT Oct. 2012 3113-3119 He, J., see Hou, D., TMTT Dec. 2012 3728-3738 He, S., and Saavedra, C. E., An Ultra-Low-Voltage and Low-Power 2 Subharmonic Downconverter Mixer; TMTT Feb. 2012 311-317 He, W., see Zhang, L., TMTT Jan. 2012 1-7 Hedge, R., see Szabo, Z., TMTT Nov. 2012 3634-3635 Heinemann, B., see Ojefors, E., TMTT May 2012 1397-1404 Helaoui, M., see El-Asmar, M., TMTT June 2012 1886-1895 Helaoui, M., see Bassam, S. A., TMTT June 2012 1990-1999 Helaoui, M., see Akbarpour, M., TMTT Sept. 2012 2863-2874 Helaoui, M., see Darraji, R., TMTT Sept. 2012 2875-2885 Helaoui, M., see Hasan, A., TMTT Aug. 2012 2644-2653 Helmi, S. R., see Chen, J.-H., TMTT Dec. 2012 4089-4096 Helmy, A. A., and Entesari, K., A 1–8-GHz Miniaturized Spectroscopy System for Permittivity Detection and Mixture Characterization of Organic Chemicals; TMTT Dec. 2012 4157-4170 Helszajn, J., A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the Turnstile Waveguide Circulator; TMTT Oct. 2012 3079-3087 Heng, C.-H., see Diao, S., TMTT Jan. 2012 120-130 Hennig, K., see Leong, K. M. K. H., TMTT April 2012 998-1005 Herricht, J., Sakalas, P., Ramonas, M., Schroter, M., Jungemann, C., Mukherjee, A., and Moebus, K. E., Systematic Compact Modeling of Correlated Noise in Bipolar Transistors; TMTT Nov. 2012 3403-3412 Heydari, P., see Jahanian, A., TMTT May 2012 1331-1341 Heydari, P., see Wang, C.-C., TMTT May 2012 1307-1320 Hirachi, Y., see Suga, R., TMTT March 2012 640-646 Hirano, Y., see Andersson, C. M., TMTT Dec. 2012 3778-3786 Hirata, A., Kosugi, T., Takahashi, H., Takeuchi, J., Togo, H., Yaita, M., Kukutsu, N., Aihara, K., Murata, K., Sato, Y., Nagatsuma, T., and Kado, Y., 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission; TMTT March 2012 881-895 Hirokawa, J., see Suga, R., TMTT March 2012 640-646 Honari, M. M., Mirzavand, R., and Abdipour, A., Corrections to "An ultrabroad-band reflection-type phase-shifter MMIC with series and parallel LC circuits" [Dec 01 2446-2452]; TMTT Nov. 2012 3633 Hone, T. M., Bensmida, S., Morris, K. A., Beach, M. A., McGeehan, J. P., Lees, J., Benedikt, J., and Tasker, P. J., Controlling Active Load–Pull in a Dual-Input Inverse Load Modulated Doherty Architecture; TMTT June 2012 1797-1804 Hong, J., see Qian, S., TMTT Sept. 2012 2799-2807 Hong, J., see Miller, A., TMTT June 2012 1577-1586 Hong, S., see Son, K. Y., TMTT Aug. 2012 2571-2580 Hong, S., see Lee, S., TMTT May 2012 1405-1412 Hong, S., see Yang, J., TMTT April 2012 1117-1125

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Hong, S., see Koo, B., TMTT Feb. 2012 340-351 Hong, W., see He, F. F., TMTT April 2012 1156-1165 Hong, W., see Gong, K., TMTT Oct. 2012 3071-3078 Hong, W., see Zhu, F., TMTT Oct. 2012 3062-3070 Hong, W., see Hou, D., TMTT Dec. 2012 3728-3738 Honjo, K., see Kawai, S., TMTT Feb. 2012 352-360 Horng, T.-S., see Chen, C.-H., TMTT May 2012 1278-1286 Horng, T.-S., see Hsiao, C.-H., TMTT June 2012 2000-2009 Horng, T.-S., see Chen, C.-T., TMTT Dec. 2012 4117-4128 Hotopan, G. R., see Fernandez Garcia, M., TMTT Aug. 2012 2494-2504 Hotopp, K. M., see Huang, Y.-T., TMTT Sept. 2012 2886-2893 Hou, D., Hong, W., Goh, W. L., Xiong, Y. Z., Arasu, M. A., He, J., Chen, J., and Madihian, M., Distributed Modeling of Six-Port Transformer for Millimeter-Wave SiGe BiCMOS Circuits Design; TMTT Dec. 2012 37283738 Hoversten, J., Schafer, S., Roberg, M., Norris, M., Maksimovic, D., and Popovic, Z., Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters; TMTT June 2012 2010-2020 Hraimel, B., Zhang, X., Liu, T., Xu, T., Nie, Q., and Shen, D., Performance Enhancement of an OFDM Ultra-Wideband Transmission-Over-Fiber Link Using a Linearized Mixed-Polarization Single-Drive X-Cut Mach–Zehnder Modulator; TMTT Oct. 2012 3328-3338 Hsiao, C.-H., Chen, C.-T., Horng, T.-S., and Peng, K.-C., Design of a Direct Conversion Transmitter to Resist Combined Effects of Power Amplifier Distortion and Local Oscillator Pulling; TMTT June 2012 2000-2009 Hsiao, F., see Tang, A., TMTT Dec. 2012 4129-4137 Hsieh, K.-A., Wu, H.-S., Tsai, K.-H., and Clive Tzuang, C.-K., A Dual-Band 10/24-GHz Amplifier Design Incorporating Dual-Frequency Complex Load Matching; TMTT June 2012 1649-1657 Hsieh, Y.-K., see Kuo, J.-L., TMTT March 2012 743-756 Hsin, Y.-M., see Lu, H.-C., TMTT March 2012 766-777 Hsin, Y.-M., see Kuo, C.-C., TMTT May 2012 1424-1436 Hsiung, W.-Y., see Kuo, J.-L., TMTT March 2012 743-756 Hsu, Y. A., see Kuo, J.-L., TMTT March 2012 743-756 Hu, F.-G., and Wang, C.-F., Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements; TMTT July 2012 2046-2054 Hu, X., see Tripodi, L., TMTT Dec. 2012 3761-3768 Huang, C., Buisman, K., Zampardi, P. J., Larson, L. E., and de Vreede, L. C. N., On the Compression and Blocking Distortion of Semiconductor-Based Varactors; TMTT Dec. 2012 3699-3709 Huang, C.-C., and Chen, Y.-C., Generalization and Reduction of Line-SeriesShunt Calibration for Broadband GaAs and CMOS On-Wafer Scattering Parameter Measurements; TMTT Dec. 2012 4138-4144 Huang, C.-H., see Chen, C.-H., TMTT May 2012 1278-1286 Huang, P.-C., Tsai, Z.-M., Lin, K.-Y., and Wang, H., A 17–35 GHz Broadband, High Efficiency PHEMT Power Amplifier Using Synthesized Transformer Matching Technique; TMTT Jan. 2012 112-119 Huang, Q.-L., see Bai, Y.-F., TMTT Aug. 2012 2417-2423 Huang, S.-L., see Lin, Y.-S., TMTT Aug. 2012 2590-2604 Huang, T.-H., see Chen, Y.-T., TMTT Jan. 2012 60-67 Huang, T.-H., see Li, M.-W., TMTT March 2012 679-685 Huang, T.-W., see Yang, H.-Y., TMTT April 2012 1057-1068 Huang, T.-W., see Li, W.-T., TMTT Aug. 2012 2512-2523 Huang, T.-W., see Kuo, Y.-H., TMTT Dec. 2012 3769-3777 Huang, T.-Y., see Kuo, J.-L., TMTT March 2012 743-756 Huang, X., and Wu, K.-L., A Broadband U-Slot Coupled Microstrip-to-Waveguide Transition; TMTT May 2012 1210-1217 Huang, X., and Wu, K.-L., A Broadband and Vialess Vertical Microstrip-toMicrostrip Transition; TMTT April 2012 938-944 Huang, Y.-T., Hotopp, K. M., Dian, B. C., and Chappell, W. J., Microwave Chemical Sensing at Room Temperature Using an Overmoded Waveguide Design; TMTT Sept. 2012 2886-2893 Huang, Y.-W., see Kuo, J.-L., TMTT March 2012 743-756 Huang, Y.-Y., Woo, W., Jeon, H., Lee, C.-H., and Kenney, J. S., Compact Wideband Linear CMOS Variable Gain Amplifier for Analog-Predistortion Power Amplifiers; TMTT Jan. 2012 68-76 Huang, Y.-Y., Jeon, H., Yoon, Y., Woo, W., Lee, C.-H., and Kenney, J. S., An Ultra-Compact, Linearly-Controlled Variable Phase Shifter Designed With a Novel RC Poly-Phase Filter; TMTT Feb. 2012 301-310 Huangfu, J., see Jiang, T., TMTT Jan. 2012 170-178 Huard, V., see Quemerais, T., TMTT April 2012 1079-1085 Hulsmann, A., see Hantscher, S., TMTT March 2012 870-880 Hung, H. A., see Darwish, A. M., TMTT April 2012 1038-1043 + Check author entry for coauthors

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Huyart, B., see de la Morena-Alvarez-Palencia, C., TMTT Aug. 2012 26342643 Huynen, I., see Hamoir, G., TMTT July 2012 2152-2157 I Ibrahim, A., see Kuester, D. G., TMTT July 2012 2248-2258 Ibrahim, A. A., see Darwish, A. M., TMTT April 2012 1038-1043 Imani, A., and Hashemi, H., Analysis and Design of Low Phase-Noise Oscillators With Nonlinear Resonators; TMTT Dec. 2012 3749-3760 Inac, O., Shin, D., and Rebeiz, G. M., A Phased Array RFIC With Built-In Self-Test Capabilities; TMTT Jan. 2012 139-148 Ioannidis, Z. C., see Savaidis, S. P., TMTT Oct. 2012 2972-2978 Ironside, C. N., see Cantu, H. I., TMTT Sept. 2012 2903-2912 Isaksson, M., see Landin, P. N., TMTT Nov. 2012 3582-3590 Isaksson, M., see Landin, P. N., TMTT June 2012 1907-1915 Ishikawa, K., see Okano, Y., TMTT Aug. 2012 2456-2464 Ishikawa, R., see Kawai, S., TMTT Feb. 2012 352-360 Islam, M. A., and Karmakar, N. C., A Novel Compact Printable Dual-Polarized Chipless RFID System; TMTT July 2012 2142-2151 Issakov, V., see Wojnowski, M., TMTT July 2012 2220-2247 Itoh, T., see Wu, C.-T. M., TMTT April 2012 1027-1037 Itoh, T., see Ueda, T., TMTT Oct. 2012 3043-3054 Itoh, T., see Sun, J. S., TMTT Dec. 2012 3950-3958 J Jabotinski, V., Chernin, D., Nguyen, K. T., Antonsen, T. M., and Levush, B., Nonperiodic Perturbations in Periodic RF Structures; TMTT April 2012 915-929 Jacob, M., Priebe, S., Dickhoff, R., Kleine-Ostmann, T., Schrader, T., and Kurner, T., Diffraction in mm and Sub-mm Wave Indoor Propagation Channels; TMTT March 2012 833-844 Jaeschke, T., see Pohl, N., TMTT March 2012 757-765 Jafari, E., see Amjadi, M., TMTT Jan. 2012 39-45 Jahanian, A., and Heydari, P., A CMOS Distributed Amplifier With Distributed Active Input Balun Using GBW and Linearity Enhancing Techniques; TMTT May 2012 1331-1341 Jahn, M., Feger, R., Wagner, C., Tong, Z., and Stelzer, A., A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar; TMTT March 2012 861-869 Jakoby, R., see Karabey, O. H., TMTT May 2012 1297-1306 Jakoby, R., see Puentes, M., TMTT June 2012 1720-1727 Jammers, R., see Trotta, S., TMTT March 2012 778-794 Janezic, M. D., see Penaranda-Foix, F. L., TMTT Sept. 2012 2730-2740 Jang, S., see Lee, S., TMTT Oct. 2012 3161-3168 Jansen, R., see Narendra, K., TMTT Oct. 2012 3189-3200 Jansen, R. H., see Sun, G., TMTT Jan. 2012 99-111 Janssen, E., see Sakian, P., TMTT March 2012 702-713 Javadzadeh, S. M. H., Mardy, Z., Mehrany, K., Farzaneh, F., and Fardmanesh, M., Fast and Efficient Analysis of Transmission Lines With Arbitrary Nonuniformities of Sub-Wavelength Scale; TMTT Aug. 2012 2378-2384 Je, M., see Diao, S., TMTT Jan. 2012 120-130 Jee, S., Moon, J., Kim, J., Son, J., and Kim, B., Switching Behavior of Class-E Power Amplifier and Its Operation Above Maximum Frequency; TMTT Jan. 2012 89-98 Jee, S., see Moon, J., TMTT June 2012 1937-1951 Jeon, H., see Huang, Y.-Y., TMTT Jan. 2012 68-76 Jeon, H., see Huang, Y.-Y., TMTT Feb. 2012 301-310 Jeong, Y., see Chaudhary, G., TMTT July 2012 2115-2123 Jerby, E., see Meir, Y., TMTT Aug. 2012 2665-2672 Jhamb, K., see Li, L., TMTT Aug. 2012 2654-2664 Jiang, P., see Chen, D., TMTT Nov. 2012 3491-3501 Jiang, S., see Kong, C., TMTT Nov. 2012 3413-3419 Jiang, T., Wang, Z., Li, D., Pan, J., Zhang, B., Huangfu, J., Salamin, Y., Li, C., and Ran, L., Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial; TMTT Jan. 2012 170-178 Jiang, Y., see Li, M., TMTT June 2012 1979-1989 Jiang, Y.-S., see Lu, H.-C., TMTT March 2012 766-777 Jin, B., Moon, J., Zhao, C., and Kim, B., A 30.8-dBm Wideband CMOS Power Amplifier With Minimized Supply Fluctuation; TMTT June 2012 16581666

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Jin, J., see Chen, D., TMTT Nov. 2012 3491-3501 John, D. L., see Nazarian, A. L., TMTT Dec. 2012 3683-3692 John, J., see Trotta, S., TMTT March 2012 778-794 Johnson, E., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Jong, T.-L., see Lin, S.-C., TMTT April 2012 975-988 Jooyaie, A., and Chang, M.-C. F., Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation; TMTT Aug. 2012 2505-2511 Jou, C. F., see Shen, I.-S., TMTT Feb. 2012 318-328 Jung, J.-Y., Park, C.-W., and Yeom, K.-W., A Novel Carrier Leakage Suppression Front-End for UHF RFID Reader; TMTT May 2012 1468-1477 Jungemann, C., see Herricht, J., TMTT Nov. 2012 3403-3412 Junping, G., see Wenzhi, W., TMTT Nov. 2012 3349-3358 K Kabir, M., and Khazaka, R., Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach; TMTT Dec. 2012 3927-3938 Kado, Y., see Ueda, T., TMTT Oct. 2012 3043-3054 Kado, Y., see Hirata, A., TMTT March 2012 881-895 Kalansuriya, P., Karmakar, N. C., and Viterbo, E., On the Detection of Frequency-Spectra-Based Chipless RFID Using UWB Impulsed Interrogation; TMTT Dec. 2012 4187-4197 Kalantari, M., see Gharibdoust, K., TMTT July 2012 2192-2202 Kalantari, N., and Buckwalter, J. F., A Nested-Reactance Feedback Power Amplifier for -Band Applications; TMTT June 2012 1667-1675 Kalim, D., see Wei, M.-D., TMTT June 2012 1916-1927 Kaminsky, D., see Perigaud, A., TMTT April 2012 965-974 Kang, B., Yim, J., Kim, T., Ko, S., Ko, W., Shin, H., Ryu, I., Yang, S.-G., Bae, J.-D., and Park, H., Design and Analysis of an Ultra-Wideband Automatic Self-Calibrating Upconverter in 65-nm CMOS; TMTT July 2012 2178-2191 Kang, D.-W., see Kim, C.-Y., TMTT March 2012 730-742 Kang, D.-W., see Shin, D., TMTT Feb. 2012 381-386 Kang, D.-W., see Kim, S. Y., TMTT Nov. 2012 3431-3439 Kang, S., see Kim, U., TMTT Aug. 2012 2532-2542 Kang, S.-Y., Ryu, S.-T., and Park, C.-S., A Precise Decibel-Linear Programmable Gain Amplifier Using a Constant Current-Density Function; TMTT Sept. 2012 2843-2850 Kang, Y.-M., see Kim, M.-G., TMTT Aug. 2012 2486-2493 Kao, J.-C., Tsai, Z.-M., Lin, K.-Y., and Wang, H., A Modified Wilkinson Power Divider With Isolation Bandwidth Improvement; TMTT Sept. 2012 27682780 Kao, K.-Y., see Kuo, J.-L., TMTT March 2012 743-756 Karabey, O. H., Gaebler, A., Strunck, S., and Jakoby, R., A 2-D Electronically Steered Phased-Array Antenna With 2 2 Elements in LC Display Technology; TMTT May 2012 1297-1306 Karmakar, N. C., see Koswatta, R. V., TMTT Sept. 2012 2925-2933 Karmakar, N. C., see Islam, M. A., TMTT July 2012 2142-2151 Karmakar, N. C., see Kalansuriya, P., TMTT Dec. 2012 4187-4197 Kasalynas, I., see Boppel, S., TMTT Dec. 2012 3834-3843 Katehi, L. P. B., see Liu, X., TMTT Feb. 2012 270-283 Kawai, S., Takayama, Y., Ishikawa, R., and Honjo, K., A High-Efficiency LowDistortion GaN HEMT Doherty Power Amplifier With a Series-Connected Load; TMTT Feb. 2012 352-360 Kearney, M. J., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Keats, B., see Yassini, B., TMTT Dec. 2012 4002-4012 Kelly, A. E., see Cantu, H. I., TMTT Sept. 2012 2903-2912 Kenney, J. S., see Huang, Y.-Y., TMTT Feb. 2012 301-310 Kenney, J. S., see Huang, Y.-Y., TMTT Jan. 2012 68-76 Kenney, J. S., see Yoon, Y., TMTT Jan. 2012 77-88 Ker, M.-D., see Lin, C.-Y., TMTT March 2012 714-723 Khan, W. T., see Patterson, C. E., TMTT Nov. 2012 3599-3607 Khazaka, R., see Kabir, M., TMTT Dec. 2012 3927-3938 Kheirdoost, A., Moradi, G., and Abdipour, A., An Analytical Formulation for Black Box Conversion Matrix Extraction; TMTT June 2012 1493-1499 Kilic, E., Siart, U., and Eibert, T. F., Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation; TMTT May 2012 1437-1443 Kim, B., see Jee, S., TMTT Jan. 2012 89-98 Kim, B., see Popovic, Z., TMTT June 2012 1753-1754

+ Check author entry for coauthors

Kim, B., see Moon, J., TMTT June 2012 1937-1951 Kim, B., see Jin, B., TMTT June 2012 1658-1666 Kim, C.-Y., see Lee, S., TMTT May 2012 1405-1412 Kim, C.-Y., Kang, D.-W., and Rebeiz, G. M., A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array; TMTT March 2012 730-742 Kim, C.-Y., see Yang, J., TMTT April 2012 1117-1125 Kim, H., see Yoon, Y., TMTT Jan. 2012 77-88 Kim, H., see Woo, S., TMTT Oct. 2012 3169-3178 Kim, J., Yu, W., and Cho, S., A Digital-Intensive Multimode Multiband Receiver Using a Sinc Filter-Embedded VCO-Based ADC; TMTT Oct. 2012 3254-3262 Kim, J., see Jee, S., TMTT Jan. 2012 89-98 Kim, J., see Yoon, Y., TMTT Jan. 2012 77-88 Kim, J., Dabag, H., Asbeck, P., and Buckwalter, J. F., -Band and -Band Power Amplifiers in 45-nm CMOS SOI; TMTT June 2012 1870-1877 Kim, J., see Moon, J., TMTT June 2012 1937-1951 Kim, J., see Moon, J., TMTT June 2012 1937-1951 Kim, J., and Silva-Martinez, J., Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications; TMTT Sept. 2012 2833-2842 Kim, J., see Kim, U., TMTT Aug. 2012 2532-2542 Kim, J. H., and Park, C. S., Analysis and Implementation of Doherty Power Amplifier With Two-Point Envelope Modulation; TMTT May 2012 13531364 Kim, M.-G., An, H.-W., Kang, Y.-M., Lee, J.-Y., and Yun, T.-Y., A LowVoltage, Low-Power, and Low-Noise UWB Mixer Using Bulk-Injection and Switched Biasing Techniques; TMTT Aug. 2012 2486-2493 Kim, S., Georgiadis, A., Collado, A., and Tentzeris, M. M., An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications; TMTT Dec. 2012 4178-4186 Kim, S. Y., Kang, D.-W., Koh, K.-J., and Rebeiz, G. M., An Improved Wideband All-Pass I/Q Network for Millimeter-Wave Phase Shifters; TMTT Nov. 2012 3431-3439 Kim, S.-G., Yun, G.-H., and Yook, J.-G., Compact Vital Signal Sensor Using Oscillation Frequency Deviation; TMTT Feb. 2012 393-400 Kim, T., see Kang, B., TMTT July 2012 2178-2191 Kim, U., Kang, S., Woo, J., Kwon, Y., and Kim, J., A Multiband Reconfigurable Power Amplifier for UMTS Handset Applications; TMTT Aug. 2012 25322542 Kim, W., see Woo, S., TMTT Oct. 2012 3169-3178 Kim, Y., see Tang, A., TMTT Dec. 2012 4129-4137 Kimball, D. F., see Kwak, M., TMTT June 2012 1850-1861 Kimball, D. F., see Hassan, M., TMTT May 2012 1321-1330 Kimball, D. F., see Presti, C. D., TMTT March 2012 604-618 Kiuru, T., see Silvonen, K., TMTT Nov. 2012 3551-3558 Kleine-Ostmann, T., see Jacob, M., TMTT March 2012 833-844 Knockaert, L., see Ferranti, F., TMTT March 2012 431-440 Knockaert, L., see Spina, D., TMTT Aug. 2012 2329-2338 Ko, S., see Kang, B., TMTT July 2012 2178-2191 Ko, W., see Kang, B., TMTT July 2012 2178-2191 Ko, Y., see Roblin, P., TMTT June 2012 1964-1978 Koh, K.-J., see Kim, S. Y., TMTT Nov. 2012 3431-3439 Kong, C., Li, H., Chen, X., Jiang, S., Zhou, J., and Chen, C., A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor; TMTT Nov. 2012 3413-3419 Koo, B., see Son, K. Y., TMTT Aug. 2012 2571-2580 Koo, B., Na, Y., and Hong, S., Integrated Bias Circuits of RF CMOS Cascode Power Amplifier for Linearity Enhancement; TMTT Feb. 2012 340-351 Kopa, A., see Xiang, B., TMTT Nov. 2012 3449-3457 Kosugi, T., see Hirata, A., TMTT March 2012 881-895 Koswatta, R. V., and Karmakar, N. C., A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading; TMTT Sept. 2012 2925-2933 Kouki, A. B., see El-Asmar, M., TMTT June 2012 1886-1895 Krozer, V., see Boppel, S., TMTT Dec. 2012 3834-3843 Kuester, D. G., Novotny, D. R., Guerrieri, J. R., Ibrahim, A., and Popovic, Z. B., Simple Test and Modeling of RFID Tag Backscatter; TMTT July 2012 2248-2258 Kukutsu, N., see Hirata, A., TMTT March 2012 881-895 Kumar, T. B., Ma, K., and Yeo, K. S., A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization; TMTT Nov. 2012 3482-3490 Kunisch, J., see Ziegler, V., TMTT Dec. 2012 4209-4219

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Kuo, C.-C., see Lu, H.-C., TMTT March 2012 766-777 Kuo, C.-C., Lu, H.-C., Lin, P.-A., Tai, C.-F., Hsin, Y.-M., and Wang, H., A Fully SiP Integrated -Band Butler Matrix End-Fire Beam-Switching Transmitter Using Flip-Chip Assembled CMOS Chips on LTCC; TMTT May 2012 1424-1436 Kuo, C.-N., see Li, C.-H., TMTT Nov. 2012 3502-3512 Kuo, H.-C., see Chen, Y.-T., TMTT Jan. 2012 60-67 Kuo, J.-J., Lien, C.-H., Tsai, Z.-M., Lin, K.-Y., Schmalz, K., Scheytt, J. C., and Wang, H., Design and Analysis of Down-Conversion Gate/Base-Pumped Harmonic Mixers Using Novel Reduced-Size 180 Hybrid With Different Input Frequencies; TMTT Aug. 2012 2473-2485 Kuo, J.-L., Lu, Y.-F., Huang, T.-Y., Chang, Y.-L., Hsieh, Y.-K., Peng, P.-J., Chang, I.-C., Tsai, T.-C., Kao, K.-Y., Hsiung, W.-Y., Wang, J., Hsu, Y. A., Lin, K.-Y., Lu, H.-C., Lin, Y.-C., Lu, L.-H., Huang, Y.-W., Wu, R.-B., and Wang, H., 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process; TMTT March 2012 743-756 Kuo, J.-L., see Kuo, N.-C., TMTT March 2012 542-554 Kuo, J.-T., see Lin, T.-W., TMTT Sept. 2012 2808-2814 Kuo, M.-C., see Li, C.-H., TMTT Nov. 2012 3502-3512 Kuo, N.-C., Kuo, J.-L., and Wang, H., Novel MMIC Power Amplifier Linearization Utilizing Input Reflected Nonlinearity; TMTT March 2012 542-554 Kuo, Y.-H., Tsai, J.-H., Huang, T.-W., and Wang, H., Design and Analysis of Digital-Assisted Bandwidth-Enhanced Miller Divider in 0.18- m CMOS Process; TMTT Dec. 2012 3769-3777 Kuo, Y.-T., and Chang, C.-Y., Analytical Design of Two-Mode Dual-Band Filters Using E-Shaped Resonators; TMTT Feb. 2012 250-260 Kurner, T., see Jacob, M., TMTT March 2012 833-844 Kuster, N., see Li, C.-H., TMTT July 2012 2267-2276 Kuta, S., see Wincza, K., TMTT May 2012 1218-1225 Kuwata, E., see Andersson, C. M., TMTT Dec. 2012 3778-3786 Kuylenstierna, D., Lai, S., Bao, M., and Zirath, H., Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology; TMTT Nov. 2012 3420-3430 Kuzuoglu, M., see Ozgun, O., TMTT June 2012 1744-1745 Kwak, M., Kimball, D. F., Presti, C. D., Scuderi, A., Santagati, C., Yan, J. J., Asbeck, P. M., and Larson, L. E., Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers; TMTT June 2012 1850-1861 Kwan, A., see Bassam, S. A., TMTT June 2012 1990-1999 Kwon, Y., see Kim, U., TMTT Aug. 2012 2532-2542

L Labrador, A., see Liberal, I., TMTT July 2012 2055-2065 Lacroix, B., see Donado Morcillo, C. A., TMTT Dec. 2012 3856-3867 Lai, S., see Kuylenstierna, D., TMTT Nov. 2012 3420-3430 Landin, P. N., see Nader, C., TMTT Nov. 2012 3571-3581 Landin, P. N., Van Moer, W., Isaksson, M., and Handel, P., Peak-Power Controlled Digital Predistorters for RF Power Amplifiers; TMTT Nov. 2012 3582-3590 Landin, P. N., Fritzin, J., Van Moer, W., Isaksson, M., and Alvandpour, A., Modeling and Digital Predistortion of Class-D Outphasing RF Power Amplifiers; TMTT June 2012 1907-1915 Lang, S. A., see Hantscher, S., TMTT March 2012 870-880 Larson, L. E., see Hassan, M., TMTT May 2012 1321-1330 Larson, L. E., see Huang, C., TMTT Dec. 2012 3699-3709 Larson, L. E., see Kwak, M., TMTT June 2012 1850-1861 Las Heras, F., see Fernandez Garcia, M., TMTT Aug. 2012 2494-2504 Laskar, J., see Woo, S., TMTT Oct. 2012 3169-3178 Laskin, E., see Dacquay, E., TMTT March 2012 813-826 Laso, M. A. G., see Arnedo, I., TMTT May 2012 1244-1257 Laso, M. A. G., see Chudzik, M., TMTT Nov. 2012 3384-3394 Lasri, T., see Haddadi, K., TMTT March 2012 574-581 Lazaro, A., see Girbau, D., TMTT Nov. 2012 3623-3632 Le Maguer, S., see Farhat, A. L., TMTT Aug. 2012 2339-2351 Lech, R., see Sorn, M., TMTT March 2012 494-501 Leduc, H. G., see Noroozian, O., TMTT May 2012 1235-1243 Lee, C.-H., see Yoon, Y., TMTT Jan. 2012 77-88 Lee, C.-H., see Huang, Y.-Y., TMTT Jan. 2012 68-76 Lee, C.-H., see Huang, Y.-Y., TMTT Feb. 2012 301-310 Lee, C.-H., see Woo, S., TMTT Oct. 2012 3169-3178 + Check author entry for coauthors

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Lee, C.-I., Lin, W.-C., and Lin, Y.-T., Modeling Inductive Behavior of MOSFET Scattering Parameter in the Breakdown Regime; TMTT March 2012 502-508 Lee, H., see Bae, J., TMTT March 2012 582-593 Lee, H.-M., Zaki, K. A., Atia, A. E., and Piloto, A. J., Design and Diagnosis of Wideband Coupled-Resonator Bandpass Filters; TMTT May 2012 12661277 Lee, J., see Naglich, E. J., TMTT May 2012 1258-1265 Lee, J., see Naglich, E. J., TMTT Jan. 2012 21-30 Lee, J., Lee, T. C., and Chappell, W. J., Lumped-Element Realization of Absorptive Bandstop Filter With Anomalously High Spectral Isolation; TMTT Aug. 2012 2424-2430 Lee, J.-C., see Meng, F.-Y., TMTT Oct. 2012 3013-3022 Lee, J.-H., see Lin, Y.-S., TMTT Aug. 2012 2590-2604 Lee, J.-W., and Chen, J.-T., A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide; TMTT Dec. 2012 3642-3655 Lee, J.-Y., see Kim, M.-G., TMTT Aug. 2012 2486-2493 Lee, O., see Yoon, Y., TMTT Jan. 2012 77-88 Lee, S., see Park, J.-H., TMTT Feb. 2012 261-269 Lee, S., Kim, C.-Y., and Hong, S., A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator; TMTT May 2012 1405-1412 Lee, S., see Ha, J., TMTT July 2012 2106-2114 Lee, S., Jang, S., and Nguyen, C., Low-Power-Consumption Wide-LockingRange Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current; TMTT Oct. 2012 3161-3168 Lee, T. C., see Lee, J., TMTT Aug. 2012 2424-2430 Lee, W., and Afshari, E., A CMOS Noise-Squeezing Amplifier; TMTT Feb. 2012 329-339 Lee, W., Adnan, M., Momeni, O., and Afshari, E., A Nonlinear Lattice for High-Amplitude Picosecond Pulse Generation in CMOS; TMTT Feb. 2012 370-380 Lee, Y., see Park, J.-H., TMTT Feb. 2012 261-269 Lee, Y., see Ha, J., TMTT July 2012 2106-2114 Lees, J., see Carrubba, V., TMTT June 2012 1928-1936 Lees, J., see Hone, T. M., TMTT June 2012 1797-1804 Leong, K. M. K. H., Hennig, K., Zhang, C., Elmadjian, R. N., Zhou, Z., Gorospe, B. S., Chang-Chien, P. P., Radisic, V., and Deal, W. R., WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology; TMTT April 2012 998-1005 Leong, K. M. K. H., see Radisic, V., TMTT March 2012 724-729 Leung, V. W., see Hassan, M., TMTT May 2012 1321-1330 Leuther, A., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Leuther, P., see Hantscher, S., TMTT March 2012 870-880 Levush, B., see Jabotinski, V., TMTT April 2012 915-929 Levush, B., see Stantchev, G., TMTT April 2012 930-937 Li, C., see Jiang, T., TMTT Jan. 2012 170-178 Li, C., see Shao, J., TMTT Aug. 2012 2410-2416 Li, C., see Sun, J., TMTT Sept. 2012 2815-2822 Li, C., see Gu, S., TMTT Dec. 2012 3877-3885 Li, C.-H., Douglas, M., Ofli, E., Chavannes, N., Balzano, Q., and Kuster, N., Mechanisms of RF Electromagnetic Field Absorption in Human Hands and Fingers; TMTT July 2012 2267-2276 Li, C.-H., Kuo, C.-N., and Kuo, M.-C., A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS; TMTT Nov. 2012 3502-3512 Li, C.-J., see Chen, C.-T., TMTT Dec. 2012 4117-4128 Li, D., see Jiang, T., TMTT Jan. 2012 170-178 Li, E. P., see Szabo, Z., TMTT Nov. 2012 3634-3635 Li, E.-P., see Dai, G.-L., TMTT Aug. 2012 2403-2409 Li, H., see Kong, C., TMTT Nov. 2012 3413-3419 Li, H., see Trotta, S., TMTT March 2012 778-794 Li, J., and Hasan, S. M. R., Pulse-Biased Low-Power Low-Phase-Noise UHF LC-QVCO for 866 MHz RFID Front-End; TMTT Oct. 2012 3120-3125 Li, L., Tan, A. E.-C., Jhamb, K., and Rambabu, K., Buried Object Characterization Using Ultra-Wideband Ground Penetrating Radar; TMTT Aug. 2012 2654-2664 Li, M., see Li, W., TMTT May 2012 1287-1296 Li, M., see Wu, J., TMTT June 2012 1587-1594 Li, M., Liu, J., Jiang, Y., and Feng, W., Complex-Chebyshev Functional Link Neural Network Behavioral Model for Broadband Wireless Power Amplifiers; TMTT June 2012 1979-1989 Li, M.-W., see Chen, Y.-T., TMTT Jan. 2012 60-67 Li, M.-W., Wang, P.-C., Huang, T.-H., and Chuang, H.-R., Low-Voltage, Wide-Locking-Range, Millimeter-Wave Divide-by-5 Injection-Locked Frequency Dividers; TMTT March 2012 679-685

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Li, W., Li, M., and Yao, J., A Narrow-Passband and Frequency-Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating; TMTT May 2012 1287-1296 Li, W., and Yao, J., A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating; TMTT June 2012 1735-1742 Li, W.-T., Tsai, J.-H., Yang, H.-Y., Chou, W.-H., Gea, S.-B., Lu, H.-C., and Huang, T.-W., Parasitic-Insensitive Linearization Methods for 60-GHz 90-nm CMOS LNAs; TMTT Aug. 2012 2512-2523 Li, X., see Ahmed, O. S., TMTT Oct. 2012 2959-2971 Liang, C., see Fu, S., TMTT March 2012 477-483 Liang, C.-H., see Sun, S.-J., TMTT Dec. 2012 3667-3673 Liao, F.-R., and Lu, S.-S., A Waveform-Dependent Phase-Noise Analysis for Edge-Combining DLL Frequency Multipliers; TMTT April 2012 1086-1096 Liberal, I., Ederra, I., Gomez-Polo, C., Labrador, A., Perez-Landazabal, J. I., and Gonzalo, R., A Comprehensive Analysis of the Absorption Spectrum of Conducting Ferromagnetic Wires; TMTT July 2012 2055-2065 Liberal, I., Ederra, I., and Gonzalo, R., Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials; TMTT Sept. 2012 2752-2759 Lichtenberger, A. W., see Chen, L., TMTT Sept. 2012 2894-2902 Lien, C.-H., see Kuo, J.-J., TMTT Aug. 2012 2473-2485 Lim, J., see Chaudhary, G., TMTT July 2012 2115-2123 Limiti, E., see Narendra, K., TMTT Oct. 2012 3189-3200 Lin, C.-H., and Chang, H.-Y., A Broadband Injection-Locking Class-E Power Amplifier; TMTT Oct. 2012 3232-3242 Lin, C.-Y., Chu, L.-W., and Ker, M.-D., ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process; TMTT March 2012 714-723 Lin, F., Chu, Q.-X., Gong, Z., and Lin, Z., Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter; TMTT May 2012 1226-1234 Lin, F., and Luong, H., Guest Editorial; TMTT Nov. 2012 3347-3348 Lin, F., Chu, Q.-X., and Wong, S. W., Authors’ reply; TMTT Sept. 2012 29352936 Lin, K.-Y., see Kuo, J.-J., TMTT Aug. 2012 2473-2485 Lin, K.-Y., see Kao, J.-C., TMTT Sept. 2012 2768-2780 Lin, K.-Y., see Huang, P.-C., TMTT Jan. 2012 112-119 Lin, K.-Y., see Kuo, J.-L., TMTT March 2012 743-756 Lin, P.-A., see Lu, H.-C., TMTT March 2012 766-777 Lin, P.-A., see Kuo, C.-C., TMTT May 2012 1424-1436 Lin, S.-C., and Jong, T.-L., Microstrip Bandpass Filters With Various Resonators Using Connected- and Edge-Coupling Mechanisms and Their Applications to Dual-Band Filters and Diplexers; TMTT April 2012 975-988 Lin, T.-W., Kuo, J.-T., and Chung, S.-J., Dual-Mode Ring Resonator Bandpass Filter With Asymmetric Inductive Coupling and Its Miniaturization; TMTT Sept. 2012 2808-2814 Lin, W.-C., see Lee, C.-I., TMTT March 2012 502-508 Lin, Y.-C., see Kuo, J.-L., TMTT March 2012 743-756 Lin, Y.-S., Lee, J.-H., Huang, S.-L., Wang, C.-H., Wang, C.-C., and Lu, S.-S., Design and Analysis of a 21–29-GHz Ultra-Wideband Receiver Front-End in 0.18- m CMOS Technology; TMTT Aug. 2012 2590-2604 Lin, Y.-T., see Lee, C.-I., TMTT March 2012 502-508 Lin, Y.-W., Lu, J.-C., and Chang, C.-Y., Design of High-Order Wideband Planar Balun Filter in -Plane Bandpass Prototype; TMTT July 2012 2124-2130 Lin, Z., see Lin, F., TMTT May 2012 1226-1234 Ling, F., see Zong, Z.-Y., TMTT June 2012 1500-1512 Linton, D., see Zelenchuk, D. E., TMTT Oct. 2012 3300-3308 Lisauskas, A., see Boppel, S., TMTT Dec. 2012 3834-3843 Liu, G., Trasser, A., and Schumacher, H., A 64–84-GHz PLL With Low Phase Noise in an 80-GHz SiGe HBT Technology; TMTT Dec. 2012 3739-3748 Liu, J., see Li, M., TMTT June 2012 1979-1989 Liu, J. Y.-C., Berenguer, R., and Chang, M.-C. F., Millimeter-Wave Self-Healing Power Amplifier With Adaptive Amplitude and Phase Linearization in 65-nm CMOS; TMTT May 2012 1342-1352 Liu, L., see Zhang, Q., TMTT April 2012 1018-1026 Liu, M., see Zhang, J., TMTT Dec. 2012 3693-3698 Liu, S.-L., Chen, K.-H., and Chin, A., A Dual-Resonant Mode 10/22-GHz VCO With a Novel Inductive Switching Approach; TMTT July 2012 2165-2177 Liu, T., see Hraimel, B., TMTT Oct. 2012 3328-3338 Liu, X., see Chen, K., TMTT Dec. 2012 3787-3797 + Check author entry for coauthors

Liu, X., Katehi, L. P. B., Chappell, W. J., and Peroulis, D., Power Handling of Electrostatic MEMS Evanescent-Mode (EVA) Tunable Bandpass Filters; TMTT Feb. 2012 270-283 Liu, Y.-J., Chen, W., Zhou, J., Zhou, B.-H., Ghannouchi, F. M., and Liu, Y.-N., Modified Least Squares Extraction for Volterra-Series Digital Predistorter in the Presence of Feedback Measurement Errors; TMTT Nov. 2012 35593570 Liu, Y.-N., see Liu, Y.-J., TMTT Nov. 2012 3559-3570 Lo, T.-L., see Wei, H.-J., TMTT June 2012 1684-1698 Lobato-Morales, H., see Sun, J. S., TMTT Dec. 2012 3950-3958 Lonac, J. A., see Florian, C., TMTT June 2012 1805-1816 Long, J. R., see Alavi, M. S., TMTT Nov. 2012 3513-3526 Long, Y., Guo, Y.-X., and Zhong, Z., A 3-D Table-Based Method for NonQuasi-Static Microwave FET Devices Modeling; TMTT Oct. 2012 30883095 Lopetegi, T., see Chudzik, M., TMTT Nov. 2012 3384-3394 Lopetegi, T., see Arnedo, I., TMTT May 2012 1244-1257 Lopez-Fernandez, I., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Lorente, J. A., see Martinez-Mendoza, M., TMTT July 2012 2131-2141 Loschonsky, M., see Chen, L., TMTT May 2012 1478-1489 Lou, J., see Wu, J., TMTT June 2012 1587-1594 Lou, J., see Wu, J., TMTT Dec. 2012 3959-3968 Lu, H., see Zhang, J., TMTT Dec. 2012 3693-3698 Lu, H.-C., see Li, W.-T., TMTT Aug. 2012 2512-2523 Lu, H.-C., see Kuo, C.-C., TMTT May 2012 1424-1436 Lu, H.-C., see Kuo, J.-L., TMTT March 2012 743-756 Lu, H.-C., Kuo, C.-C., Lin, P.-A., Tai, C.-F., Chang, Y.-L., Jiang, Y.-S., Tsai, J.-H., Hsin, Y.-M., and Wang, H., Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration; TMTT March 2012 766-777 Lu, J.-C., see Lin, Y.-W., TMTT July 2012 2124-2130 Lu, L. H., see Chen, H.-S., TMTT Jan. 2012 131-138 Lu, L.-H., see Kuo, J.-L., TMTT March 2012 743-756 Lu, S.-S., see Liao, F.-R., TMTT April 2012 1086-1096 Lu, S.-S., see Lin, Y.-S., TMTT Aug. 2012 2590-2604 Lu, X., see Chen, M. Y., TMTT Jan. 2012 179-184 Lu, Y.-F., see Kuo, J.-L., TMTT March 2012 743-756 Lucido, M., A New High-Efficient Spectral-Domain Analysis of Single and Multiple Coupled Microstrip Lines in Planarly Layered Media; TMTT July 2012 2025-2034 Lueck, M. R., see Feng, Z., TMTT July 2012 2066-2072 Lujambio, A., see Chudzik, M., TMTT Nov. 2012 3384-3394 Lujambio, A., see Arnedo, I., TMTT May 2012 1244-1257 Luong, H., see Lin, F., TMTT Nov. 2012 3347-3348 M Ma, K., see Kumar, T. B., TMTT Nov. 2012 3482-3490 Ma, X., see Sun, G., TMTT Sept. 2012 2723-2729 Maasch, M., see Puentes, M., TMTT June 2012 1720-1727 Mabrouk, K., see de la Morena-Alvarez-Palencia, C., TMTT Aug. 2012 26342643 Macchiarella, G., Oldoni, M., and Tamiazzo, S., Narrowband Microwave Filters With Mixed Topology; TMTT Dec. 2012 3980-3987 Maci, S., see Casaletti, M., TMTT Oct. 2012 2979-2989 Madihian, M., see Hou, D., TMTT Dec. 2012 3728-3738 Mahmoudi, R., see Sakian, P., TMTT March 2012 702-713 Majedi, M. S., see Pourzadi, A., TMTT Nov. 2012 3395-3402 Majied, S., see Trotta, S., TMTT March 2012 778-794 Maksimovic, D., see Hoversten, J., TMTT June 2012 2010-2020 Malo-Gomez, I., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Man, K. F., see Yeung, S. H., TMTT Sept. 2012 2760-2767 Mansour, R. R., see Ruiz-Cruz, J. A., TMTT Dec. 2012 3969-3979 Mao, J., see Xia, B., TMTT Sept. 2012 2791-2798 Mao, Y., Schmalz, K., Borngraber, J., and Scheytt, J. C., 245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology; TMTT Dec. 2012 38233833 Marante, R., see Garcia, J. A., TMTT Dec. 2012 4220-4229 Mardy, Z., see Javadzadeh, S. M. H., TMTT Aug. 2012 2378-2384 Martel, J., see Naqui, J., TMTT Oct. 2012 3023-3034 Martin, F., see Naqui, J., TMTT Oct. 2012 3023-3034 Martin-Guerrero, T. M., see Esteban, J., TMTT Aug. 2012 2385-2393

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Martinez-Mendoza, M., Ernst, C., Lorente, J. A., Alvarez-Melcon, A., and Seyfert, F., On the Relation Between Stored Energy and Fabrication Tolerances in Microwave Filters; TMTT July 2012 2131-2141 Martinez-Mendoza, M., Seyfert, F., Ernst, C., and Alvarez-Melcon, A., Formal Expression of Sensitivity and Energy Relationship in the Context of the Coupling Matrix; TMTT Nov. 2012 3369-3375 Martinez-Vazquez, M., see Ziegler, V., TMTT Dec. 2012 4209-4219 Massler, H., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Masuch, J., and Delgado-Restituto, M., A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications; TMTT May 2012 1413-1423 Masuda, T., see Nakamura, T., TMTT Sept. 2012 2823-2832 Mateo, D., see Trulls, X., TMTT Oct. 2012 3243-3253 Matsuo, M., see Parlak, M., TMTT Dec. 2012 3810-3822 Matters-Kammerer, M. K., see Tripodi, L., TMTT Dec. 2012 3761-3768 Mattes, M., see Anza, S., TMTT July 2012 2093-2105 Maulwurf, K., see Ziegler, V., TMTT Dec. 2012 4209-4219 May, G. S., see Patterson, C. E., TMTT Nov. 2012 3599-3607 Mayer, U., see Wickert, M., TMTT April 2012 1097-1104 Mayer, U., Wickert, M., Eickhoff, R., and Ellinger, F., 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers; TMTT March 2012 567-573 Maziere, C., see Demenitroux, W., TMTT June 2012 1817-1828 Mazur, J., see Sorn, M., TMTT March 2012 494-501 Mbaye, A., see de la Morena-Alvarez-Palencia, C., TMTT Aug. 2012 2634-2643 McCauley, R., see Mirotznik, M. S., TMTT Jan. 2012 158-169 McDermitt, C. S., see Diehl, J. F., TMTT Jan. 2012 195-200 McGeehan, J. P., see Hone, T. M., TMTT June 2012 1797-1804 McGeehan, J. P., see Mimis, K., TMTT Aug. 2012 2562-2570 Medi, A., see Gharibdoust, K., TMTT July 2012 2192-2202 Medina, F., see Rodriguez-Berral, R., TMTT March 2012 405-418 Medina, F., see Naqui, J., TMTT Oct. 2012 3023-3034 Medina, F., see Rodriguez-Berral, R., TMTT Dec. 2012 3908-3918 Mehrany, K., see Javadzadeh, S. M. H., TMTT Aug. 2012 2378-2384 Mei, X., see Radisic, V., TMTT March 2012 724-729 Meir, Y., and Jerby, E., Localized Rapid Heating by Low-Power Solid-State Microwave Drill; TMTT Aug. 2012 2665-2672 Meister, T. F., see Zhao, Y., TMTT Oct. 2012 3286-3299 Memarian, M., and Eleftheriades, G.V., Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings; TMTT Dec. 2012 38933907 Meng, C., see Syu, J.-S., TMTT March 2012 555-566 Meng, C., see Wei, H.-J., TMTT June 2012 1684-1698 Meng, F.-Y., Wu, Q., Erni, D., Wu, K., and Lee, J.-C., Polarization-Independent Metamaterial Analog of Electromagnetically Induced Transparency for a Refractive-Index-Based Sensor; TMTT Oct. 2012 3013-3022 Mertens, K., see Hampel, S. K., TMTT April 2012 1105-1116 Mesa, F., see Rodriguez-Berral, R., TMTT March 2012 405-418 Mesa, F., see Naqui, J., TMTT Oct. 2012 3023-3034 Mesa, F., see Rodriguez-Berral, R., TMTT Dec. 2012 3908-3918 Miller, A., and Hong, J., Cascaded Coupled Line Filter With Reconfigurable Bandwidths Using LCP Multilayer Circuit Technology; TMTT June 2012 1577-1586 Milligan, J. W., see Pengelly, R. S., TMTT June 2012 1764-1783 Milosaviljevic, S., see Evseev, S. B., TMTT Nov. 2012 3542-3550 Mimis, K., Morris, K. A., Bensmida, S., and McGeehan, J. P., Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation; TMTT Aug. 2012 2562-2570 Min, B.-W., see Ha, J., TMTT July 2012 2106-2114 Min, H., see Wang, X., TMTT Feb. 2012 387-392 Minkevicius, L., see Boppel, S., TMTT Dec. 2012 3834-3843 Mirotznik, M. S., Yarlagadda, S., McCauley, R., and Pa, P., Broadband Electromagnetic Modeling of Woven Fabric Composites; TMTT Jan. 2012 158-169 Mirzavand, R., see Honari, M. M., TMTT Nov. 2012 3633 Mittendorff, M., see Boppel, S., TMTT Dec. 2012 3834-3843 Mittra, R., see Ozgun, O., TMTT June 2012 1744-1745 Mo, T., see Chen, D., TMTT Nov. 2012 3491-3501 Moebus, K. E., see Herricht, J., TMTT Nov. 2012 3403-3412 Moeller, U., see Trotta, S., TMTT March 2012 778-794 Moez, K., see Ghadiri, A., TMTT Dec. 2012 3710-3718 Moezzi, M., see Gharibdoust, K., TMTT July 2012 2192-2202

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Moezzi, M., and Sharif Bakhtiar, M., Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths; TMTT April 2012 1069-1078 Mohammadi, S., see Chen, J.-H., TMTT Dec. 2012 4089-4096 Molero, C., see Rodriguez-Berral, R., TMTT Dec. 2012 3908-3918 Moline, D., see Trotta, S., TMTT March 2012 778-794 Momeni, O., see Lee, W., TMTT Feb. 2012 370-380 Monti, G., see De Donno, D., TMTT Sept. 2012 2693-2701 Moodie, D. G., see Rouvalis, E., TMTT March 2012 509-517 Moon, J., see Jee, S., TMTT Jan. 2012 89-98 Moon, J., Jee, S., Kim, J., Kim, J., and Kim, B., Behaviors of Class-F and Class-F Amplifiers; TMTT June 2012 1937-1951 Moon, J., see Jin, B., TMTT June 2012 1658-1666 Moquillon, L., see Quemerais, T., TMTT April 2012 1079-1085 Moradi, G., see Kheirdoost, A., TMTT June 2012 1493-1499 Morgan, D. J., see Trotta, S., TMTT March 2012 778-794 Morris, K. A., see Hone, T. M., TMTT June 2012 1797-1804 Morris, K. A., see Mimis, K., TMTT Aug. 2012 2562-2570 Mortazy, E., Chaker, M., and Wu, K., Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator; TMTT Feb. 2012 293-300 Mousavi, N., see Gharibdoust, K., TMTT July 2012 2192-2202 Mouthaan, K., see Fang, H. R., TMTT Nov. 2012 3440-3448 Mukherjee, A., see Herricht, J., TMTT Nov. 2012 3403-3412 Mundt, M., see Boppel, S., TMTT Dec. 2012 3834-3843 Murata, K., see Hirata, A., TMTT March 2012 881-895 Murphy, D., see Tang, A., TMTT Dec. 2012 4129-4137

N

Na, Y., see Koo, B., TMTT Feb. 2012 340-351 Nader, C., Landin, P. N., Van Moer, W., Bjorsell, N., Handel, P., and Ronnow, D., Peak-Power Controlling Technique for Enhancing Digital Pre-Distortion of RF Power Amplifiers; TMTT Nov. 2012 3571-3581 Nagatsuma, T., see Hirata, A., TMTT March 2012 881-895 Naglich, E. J., Lee, J., Peroulis, D., and Chappell, W. J., Extended Passband Bandstop Filter Cascade With Continuous 0.85–6.6-GHz Coverage; TMTT Jan. 2012 21-30 Naglich, E. J., Lee, J., Peroulis, D., and Chappell, W. J., Switchless Tunable Bandstop-to-All-Pass Reconfigurable Filter; TMTT May 2012 1258-1265 Naji, A., and Warr, P., Independence of the Unloaded of a Planar Electromagnetic Resonator From Its Shape; TMTT Aug. 2012 2370-2377 Nakamura, A., see Nakamura, T., TMTT Sept. 2012 2823-2832 Nakamura, T., Masuda, T., Shiramizu, N., Nakamura, A., and Washio, K., A 1.1-V Regulator-Stabilized 21.4-GHz VCO and a 115% Frequency-Range Dynamic Divider for -Band Wireless Communication; TMTT Sept. 2012 2823-2832 Nakano, H., see Suga, R., TMTT March 2012 640-646 Nakayama, M., see Andersson, C. M., TMTT Dec. 2012 3778-3786 Nakhla, M., see Ferranti, F., TMTT March 2012 431-440 Nakhla, M. S., see Saini, A. S., TMTT Nov. 2012 3359-3368 Nam, S., see Ahn, H.-R., TMTT June 2012 1549-1559 Nanver, L. K., see Evseev, S. B., TMTT Nov. 2012 3542-3550 Nanzer, J. A., Sensitivity of a Passive Correlation Interferometer to an Angularly Moving Source; TMTT Dec. 2012 3868-3876 Napijalo, V., Coupled Line 180 Hybrids With Lange Couplers; TMTT Dec. 2012 3674-3682 Naqui, J., Fernandez-Prieto, A., Duran-Sindreu, M., Mesa, F., Martel, J., Medina, F., and Martin, F., Common-Mode Suppression in Microstrip Differential Lines by Means of Complementary Split Ring Resonators: Theory and Applications; TMTT Oct. 2012 3023-3034 Narendra, K., Limiti, E., Paoloni, C., Collantes, J.-M., Jansen, R., and Yarman, S., Vectorially Combined Distributed Power Amplifiers for Software-Defined Radio Applications; TMTT Oct. 2012 3189-3200 Nassar, I. T., Weller, T. M., and Frolik, J. L., A Compact 3-D Harmonic Repeater for Passive Wireless Sensing; TMTT Oct. 2012 3309-3316 Navaratne, D., and Belostotski, L., Wideband CMOS Amplification Stage for a Direct-Sampling Square Kilometre Array Receiver; TMTT Oct. 2012 31793188 Navarro-Tapia, M., Esteban, J., Varela, J. E., and Camacho-Penalosa, C., Simulation and Measurement of the -Parameters of Obstacles in Periodic Waveguides; TMTT April 2012 1146-1155

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Nazarian, A. L., Tiemeijer, L. F., John, D. L., van Steenwijk, J. A., de Langen, M., and Pijper, R. M. T., A Physics-Based Causal Bond-Wire Model for RF Applications; TMTT Dec. 2012 3683-3692 Negra, R., see Aref, A. F., TMTT Aug. 2012 2549-2561 Negra, R., see Wei, M.-D., TMTT June 2012 1916-1927 Nemat-Nasser, S., see Bayatpur, F., TMTT April 2012 1126-1135 Nemati, H. M., see Cao, H., TMTT Feb. 2012 361-369 Ney, M., see Farhat, A. L., TMTT Aug. 2012 2339-2351 Nguyen, C., see Lee, S., TMTT Oct. 2012 3161-3168 Nguyen, H. V., see Gupta, S., TMTT Dec. 2012 3939-3949 Nguyen, K. T., see Jabotinski, V., TMTT April 2012 915-929 Nie, Q., see Hraimel, B., TMTT Oct. 2012 3328-3338 Niknejad, A. M., Chowdhury, D., and Chen, J., Design of CMOS Power Amplifiers; TMTT June 2012 1784-1796 Nikolova, N. K., see Dadash, M. S., TMTT Sept. 2012 2713-2722 Nomura, T., see Ahmed, O. S., TMTT Oct. 2012 2959-2971 Noroozian, O., Day, P. K., Eom, B. H., Leduc, H. G., and Zmuidzinas, J., Crosstalk Reduction for Superconducting Microwave Resonator Arrays; TMTT May 2012 1235-1243 Norris, M., see Hoversten, J., TMTT June 2012 2010-2020 Novotny, D. R., see Kuester, D. G., TMTT July 2012 2248-2258 O Ochoa, J. S., and Cangellaris, A. C., Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides; TMTT Dec. 2012 3919-3926 Ofli, E., see Li, C.-H., TMTT July 2012 2267-2276 Ogino, S., see Okano, Y., TMTT Aug. 2012 2456-2464 Oikonomopoulos-Zachos, C., see Ziegler, V., TMTT Dec. 2012 4209-4219 Ojefors, E., Heinemann, B., and Pfeiffer, U. R., Subharmonic 220- and 320-GHz SiGe HBT Receiver Front-Ends; TMTT May 2012 1397-1404 Ojefors, E., see Zhao, Y., TMTT Oct. 2012 3286-3299 Okamura, S., see Wang, X., TMTT April 2012 952-964 Okano, Y., Ogino, S., and Ishikawa, K., Development of Optically Transparent Ultrathin Microwave Absorber for Ultrahigh-Frequency RF Identification System; TMTT Aug. 2012 2456-2464 Oldoni, M., see Macchiarella, G., TMTT Dec. 2012 3980-3987 Oliaei, O., see Xie, H., TMTT May 2012 1390-1396 -Band MicroOliver, J. M., Rollin, J.-M., Vanhille, K., and Raman, S., A machined 3-D Cavity-Backed Patch Antenna Array With Integrated Diode Detector; TMTT Feb. 2012 284-292 Ortmanns, M., see Ostrovskyy, P., TMTT Aug. 2012 2524-2531 Ostrovskyy, P., Gustat, H., Ortmanns, M., and Scheytt, J. C., A 5-Gb/s 2.1–2.2-GHz Bandpass Modulator for Switch-Mode Power Amplifier; TMTT Aug. 2012 2524-2531 Otegi, N., Anakabe, A., Pelaz, J., Collantes, J.-M., and Soubercaze-Pun, G., Experimental Characterization of Stability Margins in Microwave Amplifiers; TMTT Dec. 2012 4145-4156 Otsuka, H., see Andersson, C. M., TMTT Dec. 2012 3778-3786 Ozgun, O., Mittra, R., and Kuzuoglu, M., Comments on “ParAFEMCap: A Parallel Adaptive Finite-Element Method for 3-D VLSI Interconnect Capacitance Extraction”; TMTT June 2012 1744-1745 Ozkeskin, F. M., Choi, S., Sarabandi, K., and Gianchandani, Y. B., An AllMetal Micro-Relay With Bulk Foil Pt–Rh Contacts for High-Power RF Applications; TMTT June 2012 1595-1604 P Pa, P., see Mirotznik, M. S., TMTT Jan. 2012 158-169 Pacheco, S., see Trotta, S., TMTT March 2012 778-794 Paganelli, R. P., see Florian, C., TMTT June 2012 1805-1816 Page, J. E., see Esteban, J., TMTT Aug. 2012 2385-2393 Pajouhi, H., see Chen, J.-H., TMTT Dec. 2012 4089-4096 Palermo, S., see Sekar, V., TMTT May 2012 1444-1455 Palmisano, G., see Giammello, V., TMTT June 2012 1676-1683 Pamarti, S., see Singhal, N., TMTT June 2012 1896-1906 Pan, J., see Jiang, T., TMTT Jan. 2012 170-178 Pan, W., see Chen, D., TMTT Nov. 2012 3491-3501 Paoloni, C., see Narendra, K., TMTT Oct. 2012 3189-3200 Papanicolaou, N. C., see Polycarpou, A. C., TMTT Oct. 2012 2950-2958 Papapolymerou, J., see Donado Morcillo, C. A., TMTT Dec. 2012 3856-3867 + Check author entry for coauthors

Papapolymerou, J., see Rebeiz, G. M., TMTT March 2012 637-639 Papapolymerou, J., see Patterson, C. E., TMTT Nov. 2012 3599-3607 Park, C. S., see Kim, J. H., TMTT May 2012 1353-1364 Park, C.-S., see Kang, S.-Y., TMTT Sept. 2012 2843-2850 Park, C.-W., see Jung, J.-Y., TMTT May 2012 1468-1477 Park, G.-H., see Szabo, Z., TMTT Nov. 2012 3634-3635 Park, H., see Kang, B., TMTT July 2012 2178-2191 Park, J.-H., Lee, S., and Lee, Y., Extremely Miniaturized Bandpass Filters Based on Asymmetric Coupled Lines With Equal Reactance; TMTT Feb. 2012 261-269 Park, M.-J., Comments on "A Compact Dual-Band 90°Coupler With CoupledLine Sections; TMTT Jan. 2012 201 Parkes, J., see Xie, H., TMTT May 2012 1390-1396 Parlak, M., Matsuo, M., and Buckwalter, J. F., Analog Signal Processing for Pulse Compression Radar in 90-nm CMOS; TMTT Dec. 2012 3810-3822 Patel, C. D., and Rebeiz, G. M., A High-Reliability High-Linearity High-Power RF MEMS Metal-Contact Switch for DC–40-GHz Applications; TMTT Oct. 2012 3096-3112 Patterson, C. E., Khan, W. T., Ponchak, G. E., May, G. S., and Papapolymerou, J., A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers; TMTT Nov. 2012 3599-3607 Patterson, C. E., see Donado Morcillo, C. A., TMTT Dec. 2012 3856-3867 Pelaez-Perez, A. M., Woodington, S., Fernandez-Barciela, M., Tasker, P. J., and Alonso, J. I., Large-Signal Oscillator Design Procedure Utilizing Analytical -Parameters Closed-Form Expressions; TMTT Oct. 2012 3126-3136 Pelaz, J., see Otegi, N., TMTT Dec. 2012 4145-4156 Penaranda-Foix, F. L., Janezic, M. D., Catala-Civera, J. M., and Canos, A. J., Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network; TMTT Sept. 2012 27302740 Peng, K.-C., see Chen, C.-T., TMTT Dec. 2012 4117-4128 Peng, K.-C., see Hsiao, C.-H., TMTT June 2012 2000-2009 Peng, P.-J., see Kuo, J.-L., TMTT March 2012 743-756 Pengelly, R. S., Wood, S. M., Milligan, J. W., Sheppard, S. T., and Pribble, W. L., A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs; TMTT June 2012 1764-1783 Perez-Landazabal, J. I., see Liberal, I., TMTT July 2012 2055-2065 Perigaud, A., Bila, S., Verdeyme, S., Baillargeat, D., and Kaminsky, D., Synthesis of Vertical Interdigital Filters Using Multilayered Technologies; TMTT April 2012 965-974 Peroulis, D., see Liu, X., TMTT Feb. 2012 270-283 Peroulis, D., see Naglich, E. J., TMTT Jan. 2012 21-30 Peroulis, D., see Naglich, E. J., TMTT May 2012 1258-1265 Peroulis, D., see Chen, K., TMTT June 2012 1829-1839 Peroulis, D., see Chen, K., TMTT Dec. 2012 4107-4116 Peroulis, D., see Chen, K., TMTT Dec. 2012 3787-3797 Perret, E., see Vena, A., TMTT Sept. 2012 2913-2924 Pfeiffer, U. R., see Zhao, Y., TMTT Oct. 2012 3286-3299 Pfeiffer, U. R., see Ojefors, E., TMTT May 2012 1397-1404 Pham, D., see Chen, M. Y., TMTT Jan. 2012 179-184 Phelps, A. D. R., see Zhang, L., TMTT Jan. 2012 1-7 Piazzon, L., see Saad, P., TMTT June 2012 1840-1849 Pijper, R. M. T., see Nazarian, A. L., TMTT Dec. 2012 3683-3692 Piloto, A. J., see Lee, H.-M., TMTT May 2012 1266-1277 Piraux, L., see Hamoir, G., TMTT July 2012 2152-2157 Pires, M. P., see Brandao Faria, J. A., TMTT Oct. 2012 2941-2949 Pirola, M., see Rubio, J. M., TMTT Aug. 2012 2543-2548 Pla, J. A., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Poh, C. H. J., see Donado Morcillo, C. A., TMTT Dec. 2012 3856-3867 Pohl, N., Jaeschke, T., and Aufinger, K., An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer; TMTT March 2012 757-765 Polycarpou, A. C., Christou, M. A., and Papanicolaou, N. C., A ModeMatching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals; TMTT Oct. 2012 2950-2958 Ponchak, G. E., Editorial; TMTT Dec. 2012 3892 Ponchak, G. E., see Patterson, C. E., TMTT Nov. 2012 3599-3607 Ponchak, G. E., 2011 RFIC Symposium Mini-Special Issue Editorial; TMTT May 2012 1185 Popovic, Z., see Hoversten, J., TMTT June 2012 2010-2020 Popovic, Z., see Dani, A., TMTT Dec. 2012 4097-4106 Popovic, Z., see Roberg, M., TMTT Dec. 2012 4043-4052 Popovic, Z., see Chisum, J. D., TMTT Aug. 2012 2605-2615 Popovic, Z., and Kim, B., Guest Editorial; TMTT June 2012 1753-1754

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Popovic, Z., see Falkenstein, E., TMTT July 2012 2277-2286 Popovic, Z. B., see Kuester, D. G., TMTT July 2012 2248-2258 Porch, A., see Rowe, D. J., TMTT June 2012 1699-1708 Poupot, M., see Chen, T., TMTT Dec. 2012 4171-4177 Pourzadi, A., Attari, A. R., and Majedi, M. S., A Directivity-Enhanced Directional Coupler Using Epsilon Negative Transmission Line; TMTT Nov. 2012 3395-3402 Presti, C. D., see Kwak, M., TMTT June 2012 1850-1861 Presti, C. D., Kimball, D. F., and Asbeck, P. M., Closed-Loop Digital Predistortion System With Fast Real-Time Adaptation Applied to a Handset WCDMA PA Module; TMTT March 2012 604-618 Pribble, W. L., see Pengelly, R. S., TMTT June 2012 1764-1783 Priebe, S., see Jacob, M., TMTT March 2012 833-844 Puentes, M., Maasch, M., Schubler, M., and Jakoby, R., Frequency Multiplexed 2-Dimensional Sensor Array Based on Split-Ring Resonators for Organic Tissue Analysis; TMTT June 2012 1720-1727 Pyo, G., see Yang, J., TMTT April 2012 1117-1125 Q Qian, S., and Hong, J., Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology; TMTT Sept. 2012 2799-2807 Qiu, C.-W., see Ding, P.-P., TMTT Feb. 2012 205-217 Quaglia, R., see Rubio, J. M., TMTT Aug. 2012 2543-2548 Quay, R., see Carrubba, V., TMTT June 2012 1928-1936 Queffelec, P., see Farhat, A. L., TMTT Aug. 2012 2339-2351 Quemerais, T., Moquillon, L., Fournier, J.-M., Benech, P., and Huard, V., Design-in-Reliable Millimeter-Wave Power Amplifiers in a 65-nm CMOS Process; TMTT April 2012 1079-1085 Quere, R., see Demenitroux, W., TMTT June 2012 1817-1828 Qureshi, J. H., see Theeuwen, S. J. C. H., TMTT June 2012 1755-1763 R Raboso, D., see Anza, S., TMTT July 2012 2093-2105 Radisic, V., Leong, K. M. K. H., Mei, X., Sarkozy, S., Yoshida, W., and Deal, W. R., Power Amplification at 0.65 THz Using InP HEMTs; TMTT March 2012 724-729 Radisic, V., see Leong, K. M. K. H., TMTT April 2012 998-1005 Ragonese, E., see Giammello, V., TMTT June 2012 1676-1683 Rahman, M., see Xie, H., TMTT May 2012 1390-1396 Rais-Zadeh, M., see Shim, Y., TMTT Aug. 2012 2439-2447 Rais-Zadeh, M., see Wu, Z., TMTT March 2012 518-527 Rakers, P., see Xie, H., TMTT May 2012 1390-1396 Raman, S., see Oliver, J. M., TMTT Feb. 2012 284-292 Raman, S., see Chen, L., TMTT March 2012 647-654 Rambabu, K., see Li, L., TMTT Aug. 2012 2654-2664 Ramirez, F., see de Cos, J., TMTT Oct. 2012 3137-3150 Ramirez, F., see Umpierrez, P., TMTT Nov. 2012 3527-3541 Ramirez, F., see Suarez, A., TMTT March 2012 528-541 Ramonas, M., see Herricht, J., TMTT Nov. 2012 3403-3412 Ramos, (FixMe)., see Girbau, D., TMTT Nov. 2012 3623-3632 Ramos, I., see Roberg, M., TMTT Dec. 2012 4043-4052 Ran, L., see Jiang, T., TMTT Jan. 2012 170-178 Rashed-Mohassel, J., see Hatefi Ardakani, H., TMTT March 2012 464-470 Rebeiz, G. M., see Kim, C.-Y., TMTT March 2012 730-742 Rebeiz, G. M., see Cetinoneri, B., TMTT March 2012 692-701 Rebeiz, G. M., see Inac, O., TMTT Jan. 2012 139-148 Rebeiz, G. M., see Shin, D., TMTT Feb. 2012 381-386 Rebeiz, G. M., Voinigescu, S. P., and Papapolymerou, J., Guest Editorial; TMTT March 2012 637-639 Rebeiz, G. M., see Kim, S. Y., TMTT Nov. 2012 3431-3439 Rebeiz, G. M., see Patel, C. D., TMTT Oct. 2012 3096-3112 Rebeiz, G. M., see Uzunkol, M., TMTT Oct. 2012 3263-3271 Rebeiz, G. M., see Cheng, C.-C., TMTT Aug. 2012 2431-2438 Rebeiz, G. M., see Grichener, A., TMTT Aug. 2012 2622-2633 Rebeiz, G. M., see Chiou, Y.-C., TMTT Feb. 2012 244-249 Reck, T. J., see Chen, L., TMTT Sept. 2012 2894-2902 Reindl, L. M., see Chen, L., TMTT May 2012 1478-1489 Ren, H., see Shao, J., TMTT Aug. 2012 2410-2416 Renaud, C. C., see Rouvalis, E., TMTT March 2012 509-517 + Check author entry for coauthors

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Renaud, C. C., see Rouvalis, E., TMTT March 2012 686-691 Reuter, R., see Trotta, S., TMTT March 2012 778-794 Reveyrand, T., see Roberg, M., TMTT Dec. 2012 4043-4052 Reynaert, P., see Francois, B., TMTT June 2012 1878-1885 Reynolds, M. S., see Thomas, S. J., TMTT April 2012 1175-1182 Riches, J., see Xie, H., TMTT May 2012 1390-1396 Rieh, J.-S., Guest Editorial; TMTT Dec. 2012 3641 Rima, S., see Girbau, D., TMTT Nov. 2012 3623-3632 Roberg, M., see Dani, A., TMTT Dec. 2012 4097-4106 Roberg, M., Reveyrand, T., Ramos, I., Falkenstein, E. A., and Popovic, Z., High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers; TMTT Dec. 2012 4043-4052 Roberg, M., see Falkenstein, E., TMTT July 2012 2277-2286 Roberg, M., see Hoversten, J., TMTT June 2012 2010-2020 Robertson, C. W., see Zhang, L., TMTT Jan. 2012 1-7 Robertson, D. A., see Gallacher, T. F., TMTT July 2012 2301-2309 Robertson, M. J., see Rouvalis, E., TMTT March 2012 509-517 Roblin, P., Root, D. E., Verspecht, J., Ko, Y., and Teyssier, J. P., New Trends for the Nonlinear Measurement and Modeling of High-Power RF Transistors and Amplifiers With Memory Effects; TMTT June 2012 1964-1978 Rodriguez-Berral, R., Medina, F., Mesa, F., and Garcia-Vigueras, M., Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs; TMTT March 2012 405-418 Rodriguez-Berral, R., Molero, C., Medina, F., and Mesa, F., Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs; TMTT Dec. 2012 3908-3918 Rolfes, I., see Hampel, S. K., TMTT April 2012 1105-1116 Rollin, J.-M., see Oliver, J. M., TMTT Feb. 2012 284-292 Romeira, B., see Cantu, H. I., TMTT Sept. 2012 2903-2912 Ronald, K., see Zhang, L., TMTT Jan. 2012 1-7 Ronghong, J., see Wenzhi, W., TMTT Nov. 2012 3349-3358 Ronnow, D., see Nader, C., TMTT Nov. 2012 3571-3581 Root, D. E., see Roblin, P., TMTT June 2012 1964-1978 Rorsman, N., see Andersson, C. M., TMTT Dec. 2012 3778-3786 Roskos, H. G., see Boppel, S., TMTT Dec. 2012 3834-3843 Roumeliotis, J. A., see Zouros, G. P., TMTT Sept. 2012 2741-2751 Rouvalis, E., Fice, M. J., Renaud, C. C., and Seeds, A. J., Millimeter-Wave Optoelectronic Mixers Based on Uni-Traveling Carrier Photodiodes; TMTT March 2012 686-691 Rouvalis, E., Renaud, C. C., Moodie, D. G., Robertson, M. J., and Seeds, A. J., Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes; TMTT March 2012 509-517 Rowe, D. J., Porch, A., Barrow, D. A., and Allender, C. J., Novel Coupling Structure for the Resonant Coaxial Probe; TMTT June 2012 1699-1708 Roy, S., Dounavis, A., and Beygi, A., Longitudinal-Partitioning-Based Waveform Relaxation Algorithm for Efficient Analysis of Distributed Transmission-Line Networks; TMTT March 2012 451-463 Roy, S. C. D., Comments on “Theoretical and Experimental Study of a New Class of Reflectionless Filter”; TMTT March 2012 632-633 Rubio Bretones, A., see Alvarez, J., TMTT Aug. 2012 2359-2369 Rubio, J. M., Fang, J., Camarchia, V., Quaglia, R., Pirola, M., and Ghione, G., 3–3.6-GHz Wideband GaN Doherty Power Amplifier Exploiting Output Compensation Stages; TMTT Aug. 2012 2543-2548 Ruehli, A. E., see Ferranti, F., TMTT March 2012 431-440 Ruiz-Cruz, J. A., Fahmi, M. M., and Mansour, R. R., Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity; TMTT Dec. 2012 3969-3979 Russell, D., and Weinreb, S., Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers; TMTT June 2012 1641-1648 Russell, D., and Weinreb, S., Cryogenic Self-Calibrating Noise Parameter Measurement System; TMTT May 2012 1456-1467 Russo, I., see Boccia, L., TMTT July 2012 2287-2300 Rydberg, A., see Tripodi, L., TMTT Dec. 2012 3761-3768 Ryu, I., see Kang, B., TMTT July 2012 2178-2191 Ryu, S.-T., see Kang, S.-Y., TMTT Sept. 2012 2843-2850

S Saad, P., Colantonio, P., Piazzon, L., Giannini, F., Andersson, K., and Fager, C., Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier; TMTT June 2012 1840-1849 Saavedra, C. E., see He, S., TMTT Feb. 2012 311-317 Sabater, J., see Ziegler, V., TMTT Dec. 2012 4209-4219

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Safarian, Z., and Hashemi, H., Passive Subharmonic Generation Using Memoryless Nonlinear Circuits; TMTT Dec. 2012 4053-4065 Saini, A. S., Nakhla, M. S., and Achar, R., Generalized Time-Domain Adjoint Sensitivity Analysis of Distributed MTL Networks; TMTT Nov. 2012 33593368 Sakagami, U., see Wang, X., TMTT April 2012 952-964 Sakalas, P., see Herricht, J., TMTT Nov. 2012 3403-3412 Sakian, P., Janssen, E., van Roermund, A. H. M., and Mahmoudi, R., Analysis and Design of a 60 GHz Wideband Voltage-Voltage Transformer Feedback LNA; TMTT March 2012 702-713 Salamin, Y., see Jiang, T., TMTT Jan. 2012 170-178 Salski, B., and Celuch, M., On the Equivalence Between the Maxwell-Garnett Mixing Rule and the Debye Relaxation Formula; TMTT Aug. 2012 23522358 Samulak, A., see Trotta, S., TMTT March 2012 778-794 Sancho, S., see Suarez, A., TMTT March 2012 528-541 Santagati, C., see Kwak, M., TMTT June 2012 1850-1861 Sarabandi, K., see Ozkeskin, F. M., TMTT June 2012 1595-1604 Sarkas, I., Hasch, J., Balteanu, A., and Voinigescu, S. P., A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna; TMTT March 2012 795-812 Sarkas, I., see Voinigescu, S. P., TMTT Dec. 2012 4024-4034 Sarkozy, S., see Radisic, V., TMTT March 2012 724-729 Sato, Y., see Hirata, A., TMTT March 2012 881-895 Sauleau, R., see Chahat, N., TMTT March 2012 827-832 Sauleau, R., see Chahat, N., TMTT July 2012 2259-2266 Sauleau, R., see Casaletti, M., TMTT Oct. 2012 2979-2989 Saunders, C. S., and Steer, M. B., Passivity Enforcement for Admittance Models of Distributed Networks Using an Inverse Eigenvalue Method; TMTT Jan. 2012 8-20 Sautreuil, B., see Dacquay, E., TMTT March 2012 813-826 Savaidis, S. P., Ioannidis, Z. C., and Stathopoulos, N. A., Hybrid Field/Transmission-Line Model for the Study of Coaxial Corrugated Waveguides; TMTT Oct. 2012 2972-2978 Schafer, S., see Hoversten, J., TMTT June 2012 2010-2020 Scheytt, J. C., see Sun, Y., TMTT Aug. 2012 2581-2589 Scheytt, J. C., see Ostrovskyy, P., TMTT Aug. 2012 2524-2531 Scheytt, J. C., see Kuo, J.-J., TMTT Aug. 2012 2473-2485 Scheytt, J. C., see Mao, Y., TMTT Dec. 2012 3823-3833 Schlechtweg, M., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Schlechtweg, M., see Hantscher, S., TMTT March 2012 870-880 Schlenther, B., see Hantscher, S., TMTT March 2012 870-880 Schmalz, K., see Mao, Y., TMTT Dec. 2012 3823-3833 Schmalz, K., see Kuo, J.-J., TMTT Aug. 2012 2473-2485 Schmitz, O., see Hampel, S. K., TMTT April 2012 1105-1116 Schnabel, R., see Hasch, J., TMTT March 2012 845-860 Schrader, T., see Jacob, M., TMTT March 2012 833-844 Schroter, M., see Herricht, J., TMTT Nov. 2012 3403-3412 Schubler, M., see Puentes, M., TMTT June 2012 1720-1727 Schulte, B., see Ziegler, V., TMTT Dec. 2012 4209-4219 Schumacher, H., see Liu, G., TMTT Dec. 2012 3739-3748 Schumacher, H., see Ulusoy, A. ., TMTT Nov. 2012 3591-3598 Schwartz, D. B., see Xie, H., TMTT May 2012 1390-1396 Scuderi, A., see Kwak, M., TMTT June 2012 1850-1861 Seeds, A. J., see Rouvalis, E., TMTT March 2012 509-517 Seeds, A. J., see Rouvalis, E., TMTT March 2012 686-691 Seelmann-Eggebert, M., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Sekar, V., Torke, W. J., Palermo, S., and Entesari, K., A Self-Sustained Microwave System for Dielectric-Constant Measurement of Lossy Organic Liquids; TMTT May 2012 1444-1455 Seliuta, D., see Boppel, S., TMTT Dec. 2012 3834-3843 Serrano, A. L. C., Correra, F. S., Vuong, T.-P., and Ferrari, P., Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control; TMTT March 2012 484-493 Sertel, K., see Apaydin, N., TMTT June 2012 1513-1519 Seyfert, F., see Martinez-Mendoza, M., TMTT July 2012 2131-2141 Seyfert, F., see Martinez-Mendoza, M., TMTT Nov. 2012 3369-3375 Shao, J., Ren, H., Arigong, B., Li, C., and Zhang, H., A Fully Symmetrical Crossover and Its Dual-Frequency Application; TMTT Aug. 2012 24102416 Sharif Bakhtiar, M., see Moezzi, M., TMTT April 2012 1069-1078 Shen, D., see Hraimel, B., TMTT Oct. 2012 3328-3338 Shen, I.-S., and Jou, C. F., A -Band Capacitor-Coupled QVCO Using Sinusoidal Current Bias Technique; TMTT Feb. 2012 318-328 + Check author entry for coauthors

Sheng, Y., see Wenzhi, W., TMTT Nov. 2012 3349-3358 Sheppard, S. T., see Pengelly, R. S., TMTT June 2012 1764-1783 Shi, X.-W., see Bai, Y.-F., TMTT Aug. 2012 2417-2423 Shie, C.-I., Cheng, J.-C., Chou, S.-C., and Chiang, Y.-C., Design of a New Type Planar Balun by Using Trans-Directional Couplers; TMTT March 2012 471-476 Shim, Y., see Wu, Z., TMTT March 2012 518-527 Shim, Y., Wu, Z., and Rais-Zadeh, M., A High-Performance Continuously Tunable MEMS Bandpass Filter at 1 GHz; TMTT Aug. 2012 2439-2447 Shin, D., Kang, D.-W., and Rebeiz, G. M., A 0.01–8-GHz (12.5 Gb/s) 4 4 CMOS Switch Matrix; TMTT Feb. 2012 381-386 Shin, D., see Inac, O., TMTT Jan. 2012 139-148 Shin, H., see Kang, B., TMTT July 2012 2178-2191 Shin, W., see Uzunkol, M., TMTT Oct. 2012 3263-3271 Shiramizu, N., see Nakamura, T., TMTT Sept. 2012 2823-2832 Shun-Meen, K., see Trotta, S., TMTT March 2012 778-794 Siart, U., see Kilic, E., TMTT May 2012 1437-1443 Silva-Martinez, J., see Kim, J., TMTT Sept. 2012 2833-2842 Silvonen, K., Dahlberg, K., and Kiuru, T., 16-Term Error Model in Reciprocal Systems; TMTT Nov. 2012 3551-3558 Sim, Y., see Chen, J.-H., TMTT Dec. 2012 4089-4096 Singhal, N., Zhang, H., and Pamarti, S., A Zero-Voltage-Switching ContourBased Outphasing Power Amplifier; TMTT June 2012 1896-1906 Smith, G. M., see Gallacher, T. F., TMTT July 2012 2301-2309 Snowden, C. M., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Snyder, R. V., see Bastioli, S., TMTT Dec. 2012 3988-4001 Soltani Tehrani, A., see Cao, H., TMTT Feb. 2012 361-369 Sommer, G., see Wojnowski, M., TMTT July 2012 2220-2247 Sommer, G., see Wojnowski, M., TMTT July 2012 2203-2219 Son, J., see Jee, S., TMTT Jan. 2012 89-98 Son, K. Y., Koo, B., and Hong, S., A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications; TMTT Aug. 2012 2571-2580 Sondena, R., see Gallacher, T. F., TMTT July 2012 2301-2309 Song, K., see Bae, J., TMTT March 2012 582-593 Sorn, M., Lech, R., and Mazur, J., Simulation and Experiment of a Compact Wideband 90 Differential Phase Shifter; TMTT March 2012 494-501 Soubercaze-Pun, G., see Otegi, N., TMTT Dec. 2012 4145-4156 Sounas, D. L., see Gupta, S., TMTT Dec. 2012 3939-3949 Sounas, D. L., and Caloz, C., Gyrotropy and Nonreciprocity of Graphene for Microwave Applications; TMTT April 2012 901-914 Spears, E., see Tombak, A., TMTT June 2012 1862-1869 Spina, D., Ferranti, F., Dhaene, T., Knockaert, L., Antonini, G., and Vande Ginste, D., Variability Analysis of Multiport Systems Via Polynomial-Chaos Expansion; TMTT Aug. 2012 2329-2338 Srisathit, K., see Worapishet, A., TMTT June 2012 1540-1548 Stake, J., see Andersson, M. A., TMTT Dec. 2012 4035-4042 Stantchev, G., Chernin, D., Antonsen, T., and Levush, B., Parallel FrequencyDomain Simulation of Hyperspectral Waveforms in Nonlinear Power Amplifiers With Memory; TMTT April 2012 930-937 Staszewski, R. B., see Alavi, M. S., TMTT Nov. 2012 3513-3526 Stathopoulos, N. A., see Savaidis, S. P., TMTT Oct. 2012 2972-2978 Steer, M. B., see Ding, M., TMTT Sept. 2012 2851-2862 Steer, M. B., see Wetherington, J. M., TMTT June 2012 1709-1719 Steer, M. B., see Feng, Z., TMTT July 2012 2066-2072 Steer, M. B., see Saunders, C. S., TMTT Jan. 2012 8-20 Stelzer, A., see Jahn, M., TMTT March 2012 861-869 Strunck, S., see Karabey, O. H., TMTT May 2012 1297-1306 Sturm, J., see Wang, X., TMTT Feb. 2012 387-392 Su, L., and Tzuang, C.-K. C., A Narrowband CMOS Ring Resonator Dual-Mode Active Bandpass Filter With Edge Periphery of 2% Free-Space Wavelength; TMTT June 2012 1605-1616 Su, T., see Sun, S.-J., TMTT Dec. 2012 3667-3673 Suarez, A., see de Cos, J., TMTT Oct. 2012 3137-3150 Suarez, A., Fernandez, E., Ramirez, F., and Sancho, S., Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes; TMTT March 2012 528-541 Subbaraman, H., see Chen, M. Y., TMTT Jan. 2012 179-184 Suga, R., Nakano, H., Hirachi, Y., Hirokawa, J., and Ando, M., A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module; TMTT March 2012 640-646 Sun, G., and Jansen, R. H., Broadband Doherty Power Amplifier via Real Frequency Technique; TMTT Jan. 2012 99-111

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Sun, G., Ma, X., and Bai, Z., Numerical Stability and Dispersion Analysis of the Precise-Integration Time-Domain Method in Lossy Media; TMTT Sept. 2012 2723-2729 Sun, J., Li, C., Geng, Y., and Wang, P., A Highly Reconfigurable Low-Power CMOS Directional Coupler; TMTT Sept. 2012 2815-2822 Sun, J. S., Lobato-Morales, H., Choi, J. H., Corona-Chavez, A., and Itoh, T., Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines; TMTT Dec. 2012 3950-3958 Sun, J. S., see Wu, C.-T. M., TMTT April 2012 1027-1037 Sun, N. X., see Wu, J., TMTT June 2012 1587-1594 Sun, N. X., see Wu, J., TMTT Dec. 2012 3959-3968 Sun, S., see Fu, S., TMTT March 2012 477-483 Sun, S.-J., Wu, B., Su, T., Deng, K., and Liang, C.-H., Wideband Dual-Mode Microstrip Filter Using Short-Ended Resonator With Centrally Loaded Inductive Stub; TMTT Dec. 2012 3667-3673 Sun, Y., Fischer, G. G., and Scheytt, J. C., A Compact Linear 60-GHz PA With 29.2% PAE Operating at Weak Avalanche Area in SiGe; TMTT Aug. 2012 2581-2589 Sun, Z., Zhang, L., Yan, Y., and Yang, H., Comments on "Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter"; TMTT Sept. 2012 2934 Sun, Z., see Gu, S., TMTT Dec. 2012 3877-3885 Surakampontorn, W., see Worapishet, A., TMTT June 2012 1540-1548 Syu, J.-S., and Meng, C., Low-Power Sub-Harmonic Direct-Conversion Receiver With Tunable RF LNA and Wideband LO Generator at U-NII Bands; TMTT March 2012 555-566 Szabo, Z., Park, G.-H., Hedge, R., and Li, E. P., Authors’ Reply to “Comments on Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship”; TMTT Nov. 2012 3634-3635

T Tai, C.-F., see Lu, H.-C., TMTT March 2012 766-777 Tai, C.-F., see Kuo, C.-C., TMTT May 2012 1424-1436 Takahashi, H., see Hirata, A., TMTT March 2012 881-895 Takahashi, K., see Wang, X., TMTT April 2012 952-964 Takayama, Y., see Kawai, S., TMTT Feb. 2012 352-360 Takeuchi, J., see Hirata, A., TMTT March 2012 881-895 Tamiazzo, S., see Macchiarella, G., TMTT Dec. 2012 3980-3987 Tan, A. E.-C., see Li, L., TMTT Aug. 2012 2654-2664 Tan, E. L., and Fan, S. Z., Graphical Analysis of Stabilization Loss and Gains for Three-Port Networks; TMTT June 2012 1635-1640 Tan, X., see Wang, X., TMTT Feb. 2012 387-392 Tang, A., Murphy, D., Hsiao, F., Virbila, G., Wang, Y.-H., Wu, H., Kim, Y., and Chang, M.-C. F., A -Band CMOS Transmitter With IF-Envelope FeedForward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer; TMTT Dec. 2012 4129-4137 Tang, X., see Fang, H. R., TMTT Nov. 2012 3440-3448 Tarlazzi, L., see Alcaro, G., TMTT Jan. 2012 185-194 Tarricone, L., see De Donno, D., TMTT Sept. 2012 2693-2701 Tartarini, G., see Alcaro, G., TMTT Jan. 2012 185-194 Tasker, P. J., see Hone, T. M., TMTT June 2012 1797-1804 Tasker, P. J., see Pelaez-Perez, A. M., TMTT Oct. 2012 3126-3136 Tasker, P. J., see Carrubba, V., TMTT June 2012 1928-1936 Teberio, F., see Chudzik, M., TMTT Nov. 2012 3384-3394 Tedjini, S., see Vena, A., TMTT Sept. 2012 2913-2924 Teizer, J., see Thomas, S. J., TMTT April 2012 1175-1182 Temple, D. S., see Feng, Z., TMTT July 2012 2066-2072 Tentzeris, M. M., see Kim, S., TMTT Dec. 2012 4178-4186 Tessmann, A., see Hantscher, S., TMTT March 2012 870-880 Teyssier, J. P., see Roblin, P., TMTT June 2012 1964-1978 Theeuwen, S. J. C. H., and Qureshi, J. H., LDMOS Technology for RF Power Amplifiers; TMTT June 2012 1755-1763 Thian, M., and Fusco, V. F., Ultrafast Low-Loss 42–70 GHz Differential SPDT Switch in 0.35 m SiGe Technology; TMTT March 2012 655-659 Thomas, S. J., Wheeler, E., Teizer, J., and Reynolds, M. S., Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems; TMTT April 2012 1175-1182 Thorsell, M., and Andersson, K., Fast Multiharmonic Active Load–Pull System With Waveform Measurement Capabilities; TMTT Jan. 2012 149-157 Tiebout, M., see Hampel, S. K., TMTT April 2012 1105-1116 Tiemeijer, L. F., see Nazarian, A. L., TMTT Dec. 2012 3683-3692 + Check author entry for coauthors

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Togo, H., see Hirata, A., TMTT March 2012 881-895 Tombak, A., Dening, D. C., Carroll, M. S., Costa, J., and Spears, E., High-Efficiency Cellular Power Amplifiers Based on a Modified LDMOS Process on Bulk Silicon and Silicon-On-Insulator Substrates With Integrated Power Management Circuitry; TMTT June 2012 1862-1869 Tomkins, A., see Dacquay, E., TMTT March 2012 813-826 Tomkins, A., see Voinigescu, S. P., TMTT Dec. 2012 4024-4034 Tong, Z., see Jahn, M., TMTT March 2012 861-869 Topak, E., see Hasch, J., TMTT March 2012 845-860 Torke, W. J., see Sekar, V., TMTT May 2012 1444-1455 Trasser, A., see Liu, G., TMTT Dec. 2012 3739-3748 Tripodi, L., Hu, X., Gotzen, R., Matters-Kammerer, M. K., van Goor, D., Cheng, S., and Rydberg, A., Broadband CMOS Millimeter-Wave Frequency Multiplier With Vivaldi Antenna in 3-D Chip-Scale Packaging; TMTT Dec. 2012 3761-3768 Trivedi, V. P., see Trotta, S., TMTT March 2012 778-794 Trotta, S., Wintermantel, M., Dixon, J., Moeller, U., Jammers, R., Hauck, T., Samulak, A., Dehlink, B., Shun-Meen, K., Li, H., Ghazinour, A., Yin, Y., Pacheco, S., Reuter, R., Majied, S., Moline, D., Aaron, T., Trivedi, V. P., Morgan, D. J., and John, J., An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology; TMTT March 2012 778-794 Trulls, X., Mateo, D., and Bofill, A., A High Dynamic-Range RF Programmable-Gain Front End for G.hn RF-Coax in 65-nm CMOS; TMTT Oct. 2012 3243-3253 Tsai, J.-H., see Li, W.-T., TMTT Aug. 2012 2512-2523 Tsai, J.-H., see Kuo, Y.-H., TMTT Dec. 2012 3769-3777 Tsai, J.-H., see Lu, H.-C., TMTT March 2012 766-777 Tsai, J.-H., Design of 40–108-GHz Low-Power and High-Speed CMOS Up-/ Down-Conversion Ring Mixers for Multistandard MMW Radio Applications; TMTT March 2012 670-678 Tsai, J.-H., see Yang, H.-Y., TMTT April 2012 1057-1068 Tsai, K.-H., see Hsieh, K.-A., TMTT June 2012 1649-1657 Tsai, T.-C., see Kuo, J.-L., TMTT March 2012 743-756 Tsai, Z.-M., see Huang, P.-C., TMTT Jan. 2012 112-119 Tsai, Z.-M., see Kuo, J.-J., TMTT Aug. 2012 2473-2485 Tsai, Z.-M., see Kao, J.-C., TMTT Sept. 2012 2768-2780 Tseng, C.-H., and Chang, C.-L., Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters; TMTT Oct. 2012 3151-3160 Tseng, C.-H., and Chang, C.-L., A Rigorous Design Methodology for Compact Planar Branch-Line and Rat-Race Couplers With Asymmetrical T-Structures; TMTT July 2012 2085-2092 Tuffy, N., Guan, L., Zhu, A., and Brazil, T. J., A Simplified Broadband Design Methodology for Linearized High-Efficiency Continuous Class-F Power Amplifiers; TMTT June 2012 1952-1963 Tzuang, C.-K. C., see Su, L., TMTT June 2012 1605-1616 U Ueda, T., Yamamoto, S., Kado, Y., and Itoh, T., Pseudo-Traveling-Wave Resonator With Magnetically Tunable Phase Gradient of Fields and Its Applications to Beam-Steering Antennas; TMTT Oct. 2012 3043-3054 Ulusoy, A. ., and Schumacher, H., Multi-Gb/s Analog Synchronous QPSK Demodulator With Phase-Noise Suppression; TMTT Nov. 2012 3591-3598 Umpierrez, P., Arana, V., and Ramirez, F., Experimental Characterization of Oscillator Circuits for Reduced-Order Models; TMTT Nov. 2012 35273541 Urick, V. J., see Diehl, J. F., TMTT Jan. 2012 195-200 Uzunkol, M., Shin, W., and Rebeiz, G. M., Design and Analysis of a LowPower 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance; TMTT Oct. 2012 3263-3271 V Valusis, G., see Boppel, S., TMTT Dec. 2012 3834-3843 van Goor, D., see Tripodi, L., TMTT Dec. 2012 3761-3768 Van Moer, W., see Nader, C., TMTT Nov. 2012 3571-3581 Van Moer, W., see Landin, P. N., TMTT Nov. 2012 3582-3590 Van Moer, W., see Landin, P. N., TMTT June 2012 1907-1915 van Roermund, A. H. M., see Sakian, P., TMTT March 2012 702-713 van Steenwijk, J. A., see Nazarian, A. L., TMTT Dec. 2012 3683-3692 Vande Ginste, D., see Spina, D., TMTT Aug. 2012 2329-2338

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Vanhille, K., see Oliver, J. M., TMTT Feb. 2012 284-292 Varela, J. E., and Esteban, J., Characterization of Waveguides With a Combination of Conductor and Periodic Boundary Contours: Application to the Analysis of Bi-Periodic Structures; TMTT March 2012 419-430 Varela, J. E., see Navarro-Tapia, M., TMTT April 2012 1146-1155 Vazquez, C., see Fernandez Garcia, M., TMTT Aug. 2012 2494-2504 Vena, A., Perret, E., and Tedjini, S., Design of Compact and Auto-Compensated Single-Layer Chipless RFID Tag; TMTT Sept. 2012 2913-2924 Ver Hoeye, S., see Fernandez Garcia, M., TMTT Aug. 2012 2494-2504 Verdeyme, S., see Perigaud, A., TMTT April 2012 965-974 Verellen, R., see Xie, H., TMTT May 2012 1390-1396 Verspecht, J., see Roblin, P., TMTT June 2012 1964-1978 Vicente, C., see Anza, S., TMTT July 2012 2093-2105 Vicente, C., see Cogollos, S., TMTT April 2012 1006-1017 Villa, E., see Aja Abelan, B., TMTT Dec. 2012 4080-4088 Villarino, R., see Girbau, D., TMTT Nov. 2012 3623-3632 Virbila, G., see Tang, A., TMTT Dec. 2012 4129-4137 Visani, D., see Alcaro, G., TMTT Jan. 2012 185-194 Visweswaran, A., see Alavi, M. S., TMTT Nov. 2012 3513-3526 Viterbo, E., see Kalansuriya, P., TMTT Dec. 2012 4187-4197 Voinigescu, S. P., Dacquay, E., Adinolfi, V., Sarkas, I., Balteanu, A., Tomkins, A., Celi, D., and Chevalier, P., Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range; TMTT Dec. 2012 4024-4034 Voinigescu, S. P., see Rebeiz, G. M., TMTT March 2012 637-639 Voinigescu, S. P., see Dacquay, E., TMTT March 2012 813-826 Voinigescu, S. P., see Sarkas, I., TMTT March 2012 795-812 Volakis, J. L., see Apaydin, N., TMTT June 2012 1513-1519 Vukusic, J., see Andersson, M. A., TMTT Dec. 2012 4035-4042 Vuong, T.-P., see Serrano, A. L. C., TMTT March 2012 484-493 W Wagner, C., see Jahn, M., TMTT March 2012 861-869 Waldschmidt, C., see Hasch, J., TMTT March 2012 845-860 Wang, C.-C., Chen, Z., and Heydari, P., W-Band Silicon-Based Frequency Synthesizers Using Injection-Locked and Harmonic Triplers; TMTT May 2012 1307-1320 Wang, C.-C., see Lin, Y.-S., TMTT Aug. 2012 2590-2604 Wang, C.-F., see Hu, F.-G., TMTT July 2012 2046-2054 Wang, C.-H., see Lin, Y.-S., TMTT Aug. 2012 2590-2604 Wang, C.-L., see Wei, H.-J., TMTT June 2012 1684-1698 Wang, H., see Kuo, C.-C., TMTT May 2012 1424-1436 Wang, H., see Kuo, J.-J., TMTT Aug. 2012 2473-2485 Wang, H., see Huang, P.-C., TMTT Jan. 2012 112-119 Wang, H., see Kuo, J.-L., TMTT March 2012 743-756 Wang, H., see Kuo, N.-C., TMTT March 2012 542-554 Wang, H., see Lu, H.-C., TMTT March 2012 766-777 Wang, H., see Yang, H.-Y., TMTT April 2012 1057-1068 Wang, H., see Kao, J.-C., TMTT Sept. 2012 2768-2780 Wang, H., see Kuo, Y.-H., TMTT Dec. 2012 3769-3777 Wang, H., see Yeh, H.-C., TMTT Dec. 2012 4066-4079 Wang, J., see Kuo, J.-L., TMTT March 2012 743-756 Wang, P., see Sun, J., TMTT Sept. 2012 2815-2822 Wang, P.-C., see Li, M.-W., TMTT March 2012 679-685 Wang, T., and Ye, Z., Robust Passive Macro-Model Generation With Local Compensation; TMTT Aug. 2012 2313-2328 Wang, T.-W., see Wei, H.-J., TMTT June 2012 1684-1698 Wang, X., Sakagami, U., Takahashi, K., and Okamura, S., A Generalized Dualand Components; Band Wilkinson Power Divider With Parallel TMTT April 2012 952-964 Wang, X., Yin, W.-Y., and Wu, K.-L., A Dual-Band Coupled-Line Coupler With an Arbitrary Coupling Coefficient; TMTT April 2012 945-951 Wang, X., Sturm, J., Yan, N., Tan, X., and Min, H., 0.6–3-GHz Wideband Receiver RF Front-End With a Feedforward Noise and Distortion Cancellation Resistive-Feedback LNA; TMTT Feb. 2012 387-392 Wang, X.-G., Cho, Y.-H., and Yun, S.-W., A Tunable Combline Bandpass Filter Loaded With Series Resonator; TMTT June 2012 1569-1576 Wang, X.-H., see Bai, Y.-F., TMTT Aug. 2012 2417-2423 Wang, Y.-C., see Weng, S.-H., TMTT Nov. 2012 3458-3473 Wang, Y.-H., see Tang, A., TMTT Dec. 2012 4129-4137 Wang, Z., see Jiang, T., TMTT Jan. 2012 170-178 Warr, P., see Naji, A., TMTT Aug. 2012 2370-2377 + Check author entry for coauthors

Webb, J. P., see Bostani, A., TMTT Sept. 2012 2677-2683 Wei, H.-J., Meng, C., Wang, T.-W., Lo, T.-L., and Wang, C.-L., 60-GHz Dual-Conversion Down-/Up-Converters Using Schottky Diode in 0.18 m Foundry CMOS Technology; TMTT June 2012 1684-1698 Wei, M.-D., Kalim, D., Erguvan, D., Chang, S.-F., and Negra, R., Investigation of Wideband Load Transformation Networks for Class-E Switching-Mode Power Amplifiers; TMTT June 2012 1916-1927 Wei, X.-C., see Dai, G.-L., TMTT Aug. 2012 2403-2409 Wei, Y. R., see Zhang, Z.-Y., TMTT March 2012 660-669 Weigel, R., see Hasch, J., TMTT March 2012 845-860 Weigel, R., see Wojnowski, M., TMTT July 2012 2220-2247 Weigel, R., see Wojnowski, M., TMTT July 2012 2203-2219 Weikle, R. M., see Chen, L., TMTT Sept. 2012 2894-2902 Weinreb, S., see Russell, D., TMTT June 2012 1641-1648 Weinreb, S., see Russell, D., TMTT May 2012 1456-1467 Weller, T. M., see Nassar, I. T., TMTT Oct. 2012 3309-3316 Weng, S.-H., Chang, H.-Y., Chiong, C.-C., and Wang, Y.-C., Gain-Bandwidth Analysis of Broadband Darlington Amplifiers in HBT-HEMT Process; TMTT Nov. 2012 3458-3473 Wenzhi, W., Sheng, Y., Xianling, L., Ronghong, J., Bird, T. S., Guo, Y. J., and Junping, G., Even- and Odd-Mode Analysis of Thick and Wide Transverse Slot in Waveguides Based on a Variational Method; TMTT Nov. 2012 33493358 Wetherington, J. M., and Steer, M. B., Robust Analog Canceller for HighDynamic-Range Radio Frequency Measurement; TMTT June 2012 17091719 Wheeler, E., see Thomas, S. J., TMTT April 2012 1175-1182 Whyte, C. G., see Zhang, L., TMTT Jan. 2012 1-7 Wickert, M., Mayer, U., and Ellinger, F., 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS; TMTT April 2012 1097-1104 Wickert, M., see Mayer, U., TMTT March 2012 567-573 Williams, K. J., see Diehl, J. F., TMTT Jan. 2012 195-200 Wincza, K., Gruszczynski, S., and Kuta, S., Approach to the Design of Asymmetric Coupled-Line Directional Couplers With the Maximum Achievable Impedance-Transformation Ratio; TMTT May 2012 1218-1225 Winnerl, S., see Boppel, S., TMTT Dec. 2012 3834-3843 Wintermantel, M., see Trotta, S., TMTT March 2012 778-794 Wochner, U., see Anza, S., TMTT July 2012 2093-2105 Wojnowski, M., Sommer, G., and Weigel, R., Device Characterization Techniques Based on Causal Relationships; TMTT July 2012 2203-2219 Wojnowski, M., Issakov, V., Sommer, G., and Weigel, R., Multimode TRL Calibration Technique for Characterization of Differential Devices; TMTT July 2012 2220-2247 Wolf, R., see Fritsche, D., TMTT Oct. 2012 3223-3231 Wolk, D., see Anza, S., TMTT July 2012 2093-2105 Wong, J., see Grebennikov, A., TMTT Oct. 2012 3214-3222 Wong, S. W., see Lin, F., TMTT Sept. 2012 2935-2936 Wong, Y. S., Zheng, S. Y., and Chan, W. S., Quasi-Arbitrary Phase-Difference Hybrid Coupler; TMTT June 2012 1530-1539 Woo, J., see Kim, U., TMTT Aug. 2012 2532-2542 Woo, S., Kim, W., Lee, C.-H., Kim, H., and Laskar, J., A Wideband Low-Power CMOS LNA With Positive–Negative Feedback for Noise, Gain, and Linearity Optimization; TMTT Oct. 2012 3169-3178 Woo, W., see Huang, Y.-Y., TMTT Feb. 2012 301-310 Woo, W., see Huang, Y.-Y., TMTT Jan. 2012 68-76 Wood, J., see Zhang, L., TMTT March 2012 441-450 Wood, J., see Chen, L., TMTT March 2012 647-654 Wood, J., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Wood, S. M., see Pengelly, R. S., TMTT June 2012 1764-1783 Woodington, S., see Pelaez-Perez, A. M., TMTT Oct. 2012 3126-3136 Worapishet, A., Srisathit, K., and Surakampontorn, W., Stepped-Impedance Coupled Resonators for Implementation of Parallel Coupled Microstrip Filters With Spurious Band Suppression; TMTT June 2012 1540-1548 Wu, B., see Fu, S., TMTT March 2012 477-483 Wu, B., see Sun, S.-J., TMTT Dec. 2012 3667-3673 Wu, C.-T. M., Dong, Y., Sun, J. S., and Itoh, T., Ring-Resonator-Inspired Power Recycling Scheme for Gain-Enhanced Distributed Amplifier-Based CRLH-Transmission Line Leaky Wave Antennas; TMTT April 2012 10271037 Wu, D. Y.-T., and Boumaiza, S., A Modified Doherty Configuration for Broadband Amplification Using Symmetrical Devices; TMTT Oct. 2012 32013213 Wu, H., see Tang, A., TMTT Dec. 2012 4129-4137 Wu, H.-S., see Hsieh, K.-A., TMTT June 2012 1649-1657

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Wu, J., Lou, J., Li, M., Yang, G., Yang, X., Adams, J., and Sun, N. X., Compact, Low-Loss, Wideband, and High-Power Handling Phase Shifters With Piezoelectric Transducer-Controlled Metallic Perturber; TMTT June 2012 1587-1594 Wu, J., Yang, X., Beguhn, S., Lou, J., and Sun, N. X., Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave; TMTT Dec. 2012 3959-3968 Wu, K., see Zhu, F., TMTT Oct. 2012 3062-3070 Wu, K., see Meng, F.-Y., TMTT Oct. 2012 3013-3022 Wu, K., see Djerafi, T., TMTT Aug. 2012 2448-2455 Wu, K., see He, F. F., TMTT April 2012 1156-1165 Wu, K., see Zhang, Z.-Y., TMTT March 2012 660-669 Wu, K., see Han, L., TMTT March 2012 619-631 Wu, K., see Mortazy, E., TMTT Feb. 2012 293-300 Wu, K.-L., see Wang, X., TMTT April 2012 945-951 Wu, K.-L., see Huang, X., TMTT April 2012 938-944 Wu, K.-L., see Huang, X., TMTT May 2012 1210-1217 Wu, L.-S., see Xia, B., TMTT Sept. 2012 2791-2798 Wu, Q., see Meng, F.-Y., TMTT Oct. 2012 3013-3022 Wu, R.-B., see Kuo, J.-L., TMTT March 2012 743-756 Wu, S.-M., see Chen, C.-H., TMTT May 2012 1278-1286 Wu, W., see Zong, Z.-Y., TMTT June 2012 1500-1512 Wu, Z., see Shim, Y., TMTT Aug. 2012 2439-2447 Wu, Z., Shim, Y., and Rais-Zadeh, M., Miniaturized UWB Filters Integrated With Tunable Notch Filters Using a Silicon-Based Integrated Passive Device Technology; TMTT March 2012 518-527 X Xia, B., Wu, L.-S., and Mao, J., A New Balanced-to-Balanced Power Divider/ Combiner; TMTT Sept. 2012 2791-2798 Xia, M.-Y., see Dai, G.-L., TMTT Aug. 2012 2403-2409 Xiang, B., Kopa, A., Fu, Z., and Apsel, A. B., Theoretical Analysis and Practical Considerations for the Integrated Time-Stretching System Using Dispersive Delay Line (DDL); TMTT Nov. 2012 3449-3457 Xiang, J., see Xie, H., TMTT May 2012 1390-1396 Xianling, L., see Wenzhi, W., TMTT Nov. 2012 3349-3358 Xie, H., Oliaei, O., Rakers, P., Fernandez, R., Xiang, J., Parkes, J., Riches, J., Verellen, R., Rahman, M., Bhan, V., and Schwartz, D. B., Single-Chip Multiband EGPRS and SAW-Less LTE WCDMA CMOS Receiver With Diversity; TMTT May 2012 1390-1396 Xiong, Y. Z., see Hou, D., TMTT Dec. 2012 3728-3738 Xiong, Y.-Z., see He, J., TMTT Oct. 2012 3113-3119 Xu, T., see Hraimel, B., TMTT Oct. 2012 3328-3338 Xu, Y., and Bosisio, R. G., Design of Multiway Power Divider by Using Stepped-Impedance Transformers; TMTT Sept. 2012 2781-2790 Xu, Z., see Gu, Q. J., TMTT May 2012 1365-1374 Xue, Q, see Chen, S., TMTT Nov. 2012 3474-3481 Xue, Q., see Yeung, S. H., TMTT Sept. 2012 2760-2767 Y Yaita, M., see Hirata, A., TMTT March 2012 881-895 Yamamoto, S., see Ueda, T., TMTT Oct. 2012 3043-3054 Yamanaka, K., see Andersson, C. M., TMTT Dec. 2012 3778-3786 Yan, J. J., see Kwak, M., TMTT June 2012 1850-1861 Yan, N., see Wang, X., TMTT Feb. 2012 387-392 Yan, Y., see Sun, Z., TMTT Sept. 2012 2934 Yang, C.-L., Chiang, M.-C., Chiu, H.-C., and Chiang, Y.-C., Design and Analysis of a Tri-Band Dual-Mode Chip Filter for 60-, 77-, and 100-GHz Applications; TMTT April 2012 989-997 Yang, G., see Wu, J., TMTT June 2012 1587-1594 Yang, H., see Sun, Z., TMTT Sept. 2012 2934 Yang, H.-Y., see Li, W.-T., TMTT Aug. 2012 2512-2523 Yang, H.-Y., Tsai, J.-H., Huang, T.-W., and Wang, H., Analysis of a New 33–58-GHz Doubly Balanced Drain Mixer in 90-nm CMOS Technology; TMTT April 2012 1057-1068 Yang, J., Pyo, G., Kim, C.-Y., and Hong, S., A 24-GHz CMOS UWB Radar Transmitter With Compressed Pulses; TMTT April 2012 1117-1125 Yang, S.-G., see Kang, B., TMTT July 2012 2178-2191 Yang, X., see Wu, J., TMTT June 2012 1587-1594 Yang, X., see Wu, J., TMTT Dec. 2012 3959-3968 Yao, J., see Li, W., TMTT June 2012 1735-1742 + Check author entry for coauthors

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Yao, J., see Li, W., TMTT May 2012 1287-1296 Yarlagadda, S., see Mirotznik, M. S., TMTT Jan. 2012 158-169 Yarman, S., see Narendra, K., TMTT Oct. 2012 3189-3200 -Band Fully Tunable Cavity Filter; Yassini, B., Yu, M., and Keats, B., A TMTT Dec. 2012 4002-4012 Yau, K. H. K., see Dacquay, E., TMTT March 2012 813-826 Ye, Z., see Wang, T., TMTT Aug. 2012 2313-2328 Yeh, H.-C., Chiong, C.-C., Aloui, S., and Wang, H., Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique; TMTT Dec. 2012 4066-4079 Yeh, Y.-L., and Chang, H.-Y., Design and Analysis of a -band Divide-byThree Injection-Locked Frequency Divider Using Second Harmonic Enhancement Technique; TMTT June 2012 1617-1625 Yeo, K. S., see Kumar, T. B., TMTT Nov. 2012 3482-3490 Yeo, S. P., see Ding, P.-P., TMTT Feb. 2012 205-217 Yeom, K.-W., see Jung, J.-Y., TMTT May 2012 1468-1477 Yeung, S., see Cheng, K.-K. M., TMTT Oct. 2012 3055-3061 Yeung, S. H., Xue, Q., and Man, K. F., Broadband 90 Differential Phase Shifter Constructed Using a Pair of Multisection Radial Line Stubs; TMTT Sept. 2012 2760-2767 Yim, J., see Kang, B., TMTT July 2012 2178-2191 Yin, W.-Y., see Wang, X., TMTT April 2012 945-951 Yin, Y., see Trotta, S., TMTT March 2012 778-794 Yoo, H.-Y., see Bae, J., TMTT March 2012 582-593 Yook, J.-G., see Kim, S.-G., TMTT Feb. 2012 393-400 Yoon, Y., Kim, J., Kim, H., An, K. H., Lee, O., Lee, C.-H., and Kenney, J. S., A Dual-Mode CMOS RF Power Amplifier With Integrated Tunable Matching Network; TMTT Jan. 2012 77-88 Yoon, Y., see Huang, Y.-Y., TMTT Feb. 2012 301-310 Yoshida, W., see Radisic, V., TMTT March 2012 724-729 You, C. J., see Gong, K., TMTT Oct. 2012 3071-3078 Young, A. R., see Zhang, L., TMTT Jan. 2012 1-7 Young, J. C., see Zhao, B., TMTT Sept. 2012 2684-2692 Yu, C., and Zhu, A., A Single Envelope Modulator-Based Envelope-Tracking Structure for Multiple-Input and Multiple-Output Wireless Transmitters; TMTT Oct. 2012 3317-3327 Yu, C., Guan, L., Zhu, E., and Zhu, A., Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers; TMTT Dec. 2012 4198-4208 Yu, M., see Yassini, B., TMTT Dec. 2012 4002-4012 Yu, W., see Kim, J., TMTT Oct. 2012 3254-3262 Yuan, C.-W., see Zhang, Q., TMTT April 2012 1018-1026 Yuan, X., see Diao, S., TMTT Jan. 2012 120-130 Yun, G.-H., see Kim, S.-G., TMTT Feb. 2012 393-400 Yun, S.-W., see Wang, X.-G., TMTT June 2012 1569-1576 Yun, T.-Y., see Kim, M.-G., TMTT Aug. 2012 2486-2493

Z Zaki, K. A., see Lee, H.-M., TMTT May 2012 1266-1277 Zampardi, P. J., see Huang, C., TMTT Dec. 2012 3699-3709 Zappelli, L., An Equivalent Circuit for Discontinuities Exciting Evanescent Accessible Modes; TMTT May 2012 1197-1209 Zelenchuk, D. E., Fusco, V., Goussetis, G., Mendez, A., and Linton, D., Millimeter-Wave Printed Circuit Board Characterization Using Substrate Integrated Waveguide Resonators; TMTT Oct. 2012 3300-3308 Zeng, X., see Chen, G., TMTT Feb. 2012 218-231 Zeng, X., see Chen, G., TMTT June 2012 1745-1747 Zhadobov, M., see Chahat, N., TMTT July 2012 2259-2266 Zhadobov, M., see Chahat, N., TMTT March 2012 827-832 Zhang, B., see Jiang, T., TMTT Jan. 2012 170-178 Zhang, C., see Leong, K. M. K. H., TMTT April 2012 998-1005 Zhang, C., see Chen, L., TMTT Sept. 2012 2894-2902 Zhang, H., see Shao, J., TMTT Aug. 2012 2410-2416 Zhang, H., see Singhal, N., TMTT June 2012 1896-1906 Zhang, J., Zhang, Y., Lu, H., Zhang, Y., and Liu, M., A Novel Model for Implementation of Gamma Radiation Effects in GaAs HBTs; TMTT Dec. 2012 3693-3698 Zhang, L., see Sun, Z., TMTT Sept. 2012 2934 Zhang, L., see Aaen, P. H., TMTT Dec. 2012 4013-4023 Zhang, L., see Apaydin, N., TMTT June 2012 1513-1519 Zhang, L., He, W., Ronald, K., Phelps, A. D. R., Whyte, C. G., Robertson, C. W., Young, A. R., Donaldson, C. R., and Cross, A. W., Multi-Mode

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Coupling Wave Theory for Helically Corrugated Waveguide; TMTT Jan. 2012 1-7 Zhang, L., Aaen, P. H., and Wood, J., Portable Space Mapping for Efficient Statistical Modeling of Passive Components; TMTT March 2012 441-450 Zhang, Q., Yuan, C.-W., and Liu, L., Theoretical Design and Analysis for – Rectangular Waveguide Mode Converters; TMTT April 2012 1018-1026 Zhang, Q., Gupta, S., and Caloz, C., Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay; TMTT Aug. 2012 23942402 Zhang, Q., see Gupta, S., TMTT Dec. 2012 3939-3949 Zhang, X., see Hraimel, B., TMTT Oct. 2012 3328-3338 Zhang, Y., see Gong, K., TMTT Oct. 2012 3071-3078 Zhang, Y., see Zhang, J., TMTT Dec. 2012 3693-3698 Zhang, Y., see Zhang, J., TMTT Dec. 2012 3693-3698 Zhang, Y. P., see He, J., TMTT Oct. 2012 3113-3119 Zhang, Y.-J., and Fan, J., A Generalized Multiple Scattering Method for Dense Vias With Axially Anisotropic Modes in an Arbitrarily Shaped Plate Pair; TMTT July 2012 2035-2045 Zhang, Z.-Y., Wei, Y. R., and Wu, K., Broadband Millimeter-Wave Single Balanced Mixer and Its Applications to Substrate Integrated Wireless Systems; TMTT March 2012 660-669 Zhao, B., Young, J. C., and Gedney, S. D., SPICE Lumped Circuit Subcell Model for the Discontinuous Galerkin Finite-Element Time-Domain Method; TMTT Sept. 2012 2684-2692 Zhao, C., see Jin, B., TMTT June 2012 1658-1666 Zhao, J., In Vitro Dosimetry and Temperature Evaluations of a Typical Millimeter-Wave Aperture-Field Exposure Setup; TMTT Nov. 2012 3608-3622 Zhao, Y., Ojefors, E., Aufinger, K., Meister, T. F., and Pfeiffer, U. R., A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology; TMTT Oct. 2012 3286-3299 Zheng, S. Y., see Wong, Y. S., TMTT June 2012 1530-1539 Zheng, Y., see Diao, S., TMTT Jan. 2012 120-130 Zhong, Z., see Long, Y., TMTT Oct. 2012 3088-3095 Zhou, B.-H., see Liu, Y.-J., TMTT Nov. 2012 3559-3570 Zhou, J., see Kong, C., TMTT Nov. 2012 3413-3419 Zhou, J., see Chen, D., TMTT Nov. 2012 3491-3501 Zhou, J., see Liu, Y.-J., TMTT Nov. 2012 3559-3570 Zhou, Z., see Leong, K. M. K. H., TMTT April 2012 998-1005 Zhu, A., see Guan, L., TMTT March 2012 594-603 Zhu, A., see Tuffy, N., TMTT June 2012 1952-1963 Zhu, A., see Yu, C., TMTT Oct. 2012 3317-3327 Zhu, A., see Yu, C., TMTT Dec. 2012 4198-4208 Zhu, E., see Yu, C., TMTT Dec. 2012 4198-4208 Zhu, F., Hong, W., Chen, J.-X., and Wu, K., Ultra-Wideband Single and Dual Baluns Based on Substrate Integrated Coaxial Line Technology; TMTT Oct. 2012 3062-3070 Zhu, H., see Chen, G., TMTT June 2012 1745-1747 Zhu, H., see Chen, G., TMTT Feb. 2012 218-231 Ziegler, V., Schulte, B., Sabater, J., Bovelli, S., Kunisch, J., Maulwurf, K., Martinez-Vazquez, M., Oikonomopoulos-Zachos, C., Glisic, S., Ehrig, M., and Grass, E., Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin; TMTT Dec. 2012 4209-4219 Zirath, H., see Kuylenstierna, D., TMTT Nov. 2012 3420-3430 Zmuidzinas, J., see Noroozian, O., TMTT May 2012 1235-1243 Zong, Z.-Y., Wu, W., Ling, F., Chen, J., and Fang, D.-G., Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM; TMTT June 2012 1500-1512 Zouhdi, S., see Ding, P.-P., TMTT Feb. 2012 205-217 Zouros, G. P., and Roumeliotis, J. A., Exact and Closed-Form Cutoff Wavenumbers of Elliptical Dielectric Waveguides; TMTT Sept. 2012 2741-2751 Zwick, T., see Hasch, J., TMTT March 2012 845-860 SUBJECT INDEX

1/f

1/f noise -Band Total Power Radiometer Performance Optimization in an SiGe HBT Technology. Dacquay, E., +, TMTT March 2012 813-826 + Check author entry for coauthors

3G 3G mobile communication A Multiband Reconfigurable Power Amplifier for UMTS Handset Applications. Kim, U., +, TMTT Aug. 2012 2532-2542 Digital Predistortion Using a Vector-Switched Model. Afsardoost, S., +, TMTT April 2012 1166-1174 4G 4G mobile communication A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications. Hassan, M., +, TMTT May 2012 1321-1330 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 A Absorbing media Numerical Stability and Dispersion Analysis of the Precise-Integration Time-Domain Method in Lossy Media. Sun, G., +, TMTT Sept. 2012 2723-2729 Absorption A Comprehensive Analysis of the Absorption Spectrum of Conducting Ferromagnetic Wires. Liberal, I., +, TMTT July 2012 2055-2065 Accuracy Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers. Yu, C., +, TMTT Dec. 2012 4198-4208 Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides. Ochoa, J. S., +, TMTT Dec. 2012 3919-3926 Active antenna arrays A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 A Dual-Band Parallel Doherty Power Amplifier for Wireless Applications. Grebennikov, A., +, TMTT Oct. 2012 3214-3222 Active filters A Narrowband CMOS Ring Resonator Dual-Mode Active Bandpass Filter With Edge Periphery of 2% Free-Space Wavelength. Su, L., +, TMTT June 2012 1605-1616 Active networks Design of a New Type Planar Balun by Using Trans-Directional Couplers. Shie, C.-I., +, TMTT March 2012 471-476 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Adaptive antenna arrays Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Adaptive control A Fully Integrated Adaptive Multiband Multimode Switching-Mode CMOS Power Amplifier. Aref, A. F., +, TMTT Aug. 2012 2549-2561 Algebra Exact and Closed-Form Cutoff Wavenumbers of Elliptical Dielectric Waveguides. Zouros, G. P., +, TMTT Sept. 2012 2741-2751 All-pass filters An Improved Wideband All-Pass I/Q Network for Millimeter-Wave Phase Shifters. Kim, S. Y., +, TMTT Nov. 2012 3431-3439 Switchless Tunable Bandstop-to-All-Pass Reconfigurable Filter. Naglich, E. J., +, TMTT May 2012 1258-1265 Aluminium compounds A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 AlGaN/GaN HEMT With Distributed Gate for Channel Temperature Reduction. Darwish, A. M., +, TMTT April 2012 1038-1043 Amplification A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array. Kim, C.-Y., +, TMTT March 2012 730-742

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Amplifiers A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array. Kim, C.-Y., +, TMTT March 2012 730-742 A CMOS Noise-Squeezing Amplifier. Lee, W., +, TMTT Feb. 2012 329-339 Graphical Analysis of Stabilization Loss and Gains for Three-Port Networks. Tan, E. L., +, TMTT June 2012 1635-1640 Reconfigurable Dual-Channel Multiband RF Receiver for GPS/ Galileo/BD-2 Systems. Chen, D., +, TMTT Nov. 2012 3491-3501 Amplitude modulation Design of CMOS Power Amplifiers. Niknejad, A. M., +, TMTT June 2012 1784-1796 Amplitude shift keying Design and Analysis of a Low-Power 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance. Uzunkol, M., +, TMTT Oct. 2012 32633271 Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems. Thomas, S. J., +, TMTT April 2012 1175-1182 Analog circuits Direct Baseband I-Q Regeneration Method for Five-Port Receivers Improving DC-Offset and Second-Order Intermodulation Distortion Rejection. de la Morena-Alvarez-Palencia, C., +, TMTT Aug. 2012 2634-2643 Analog integrated circuits A Fully Integrated Adaptive Multiband Multimode Switching-Mode CMOS Power Amplifier. Aref, A. F., +, TMTT Aug. 2012 2549-2561 Analog-digital conversion A Digital-Intensive Multimode Multiband Receiver Using a Sinc FilterEmbedded VCO-Based ADC. Kim, J., +, TMTT Oct. 2012 3254-3262 Peak-Power Controlled Digital Predistorters for RF Power Amplifiers. Landin, P. N., +, TMTT Nov. 2012 3582-3590 Reconfigurable Dual-Channel Multiband RF Receiver for GPS/ Galileo/BD-2 Systems. Chen, D., +, TMTT Nov. 2012 3491-3501 Angular velocity Sensitivity of a Passive Correlation Interferometer to an Angularly Moving Source. Nanzer, J. A., +, TMTT Dec. 2012 3868-3876 Anisotropic media Numerical Stability and Dispersion Analysis of the Precise-Integration Time-Domain Method in Lossy Media. Sun, G., +, TMTT Sept. 2012 2723-2729 Rigorous Derivation and Fast Solution of Spatial-Domain Green’s Functions for Uniaxial Anisotropic Multilayers Using Modified Fast Hankel Transform Method. Ding, P.-P., +, TMTT Feb. 2012 205-217 Antenna arrays A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar. Jahn, M., +, TMTT March 2012 861-869 A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module. Suga, R., +, TMTT March 2012 640-646 An Ultra-Thin, High-Power, and Multilayer Organic Antenna Array With T/R Functionality in the -Band. Donado Morcillo, C. A., +, TMTT Dec. 2012 3856-3867 Antenna feeds A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Antenna measurements An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications. Kim, S., +, TMTT Dec. 2012 4178-4186 Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin. Ziegler, V., +, TMTT Dec. 2012 4209-4219 Broadband CMOS Millimeter-Wave Frequency Multiplier With Vivaldi Antenna in 3-D Chip-Scale Packaging. Tripodi, L., +, TMTT Dec. 2012 37613768 Antenna phased arrays 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 A 2-D Electronically Steered Phased-Array Antenna With 2 2 Elements in LC Display Technology. Karabey, O. H., +, TMTT May 2012 1297-1306 A Phased Array RFIC With Built-In Self-Test Capabilities. Inac, O., +, TMTT Jan. 2012 139-148 + Check author entry for coauthors

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Conformal Ink-Jet Printed -Band Phased-Array Antenna Incorporating Carbon Nanotube Field-Effect Transistor Based Reconfigurable True-Time Delay Lines. Chen, M. Y., +, TMTT Jan. 2012 179-184 Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Antenna radiation patterns A -Band Micromachined 3-D Cavity-Backed Patch Antenna Array With Integrated Diode Detector. Oliver, J. M., +, TMTT Feb. 2012 284-292 A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module. Suga, R., +, TMTT March 2012 640-646 Pseudo-Traveling-Wave Resonator With Magnetically Tunable Phase Gradient of Fields and Its Applications to Beam-Steering Antennas. Ueda, T., +, TMTT Oct. 2012 3043-3054 Antennas 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission. Hirata, A., +, TMTT March 2012 881-895 Autoregressive Modeling of Mobile Radio Propagation Channel in Building Ruins. Chen, L., +, TMTT May 2012 1478-1489 CMOS Integrated Antenna-Coupled Field-Effect Transistors for the Detection of Radiation From 0.2 to 4.3 THz. Boppel, S., +, TMTT Dec. 2012 3834-3843 Millimeter-Wave Technology for Automotive Radar Sensors in the 77 GHz Frequency Band. Hasch, J., +, TMTT March 2012 845-860 Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems. Thomas, S. J., +, TMTT April 2012 1175-1182 Sensitivity of a Passive Correlation Interferometer to an Angularly Moving Source. Nanzer, J. A., +, TMTT Dec. 2012 3868-3876 Apertures Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT Dec. 2012 3908-3918 Terahertz Aperture Synthesized Imaging With Fan-Beam Scanning for Personnel Screening. Gu, S., +, TMTT Dec. 2012 3877-3885 Approximation methods A Physics-Based Causal Bond-Wire Model for RF Applications. Nazarian, A. L., +, TMTT Dec. 2012 3683-3692 A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide. Lee, J.-W., +, TMTT Dec. 2012 3642-3655 Authors’ reply. Chen, G., +, TMTT June 2012 1745-1747 Array signal processing A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar. Jahn, M., +, TMTT March 2012 861-869 A Fully Integrated 0.18- m CMOS Transceiver Chip for -Band PhasedArray Systems. Gharibdoust, K., +, TMTT July 2012 2192-2202 Arrays An Ultra-Thin, High-Power, and Multilayer Organic Antenna Array With T/R Functionality in the -Band. Donado Morcillo, C. A., +, TMTT Dec. 2012 3856-3867 Attenuation Variable Reflection-Type Attenuators Based on Varactor Diodes. Bulja, S., +, TMTT Dec. 2012 3719-3727 Attenuators Variable Reflection-Type Attenuators Based on Varactor Diodes. Bulja, S., +, TMTT Dec. 2012 3719-3727 Automatic gain control A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490 Reconfigurable Dual-Channel Multiband RF Receiver for GPS/ Galileo/BD-2 Systems. Chen, D., +, TMTT Nov. 2012 3491-3501 Automotive electronics An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Autoregressive processes Autoregressive Modeling of Mobile Radio Propagation Channel in Building Ruins. Chen, L., +, TMTT May 2012 1478-1489 Avalanche breakdown in the Modeling Inductive Behavior of MOSFET Scattering Parameter Breakdown Regime. Lee, C.-I., +, TMTT March 2012 502-508

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B Backscatter On the Detection of Frequency-Spectra-Based Chipless RFID Using UWB Impulsed Interrogation. Kalansuriya, P., +, TMTT Dec. 2012 4187-4197 Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems. Thomas, S. J., +, TMTT April 2012 1175-1182 Simple Test and Modeling of RFID Tag Backscatter. Kuester, D. G., +, TMTT July 2012 2248-2258 Ball grid arrays A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module. Suga, R., +, TMTT March 2012 640-646 Baluns A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A CMOS Distributed Amplifier With Distributed Active Input Balun Using GBW and Linearity Enhancing Techniques. Jahanian, A., +, TMTT May 2012 1331-1341 Analysis of a New 33–58-GHz Doubly Balanced Drain Mixer in 90-nm CMOS Technology. Yang, H.-Y., +, TMTT April 2012 1057-1068 Design and Analysis of a 21–29-GHz Ultra-Wideband Receiver Front-End in 0.18- m CMOS Technology. Lin, Y.-S., +, TMTT Aug. 2012 2590-2604 Design of a New Type Planar Balun by Using Trans-Directional Couplers. Shie, C.-I., +, TMTT March 2012 471-476 Design of High-Order Wideband Planar Balun Filter in -Plane Bandpass Prototype. Lin, Y.-W., +, TMTT July 2012 2124-2130 Ultra-Wideband Single and Dual Baluns Based on Substrate Integrated Coaxial Line Technology. Zhu, F., +, TMTT Oct. 2012 3062-3070 Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Band-pass filters A High-Performance Continuously Tunable MEMS Bandpass Filter at 1 GHz. Shim, Y., +, TMTT Aug. 2012 2439-2447 A Narrow-Passband and Frequency-Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT May 2012 1287-1296 A Narrowband CMOS Ring Resonator Dual-Mode Active Bandpass Filter With Edge Periphery of 2% Free-Space Wavelength. Su, L., +, TMTT June 2012 1605-1616 A Quasi Elliptic Function 1.75–2.25 GHz 3-Pole Bandpass Filter With Bandwidth Control. Chiou, Y.-C., +, TMTT Feb. 2012 244-249 A Tunable Combline Bandpass Filter Loaded With Series Resonator. Wang, X.-G., +, TMTT June 2012 1569-1576 A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 Analytical Design of Two-Mode Dual-Band Filters Using E-Shaped Resonators. Kuo, Y.-T., +, TMTT Feb. 2012 250-260 Cascaded Coupled Line Filter With Reconfigurable Bandwidths Using LCP Multilayer Circuit Technology. Miller, A., +, TMTT June 2012 1577-1586 Common-Mode Suppression in Microstrip Differential Lines by Means of Complementary Split Ring Resonators: Theory and Applications. Naqui, J., +, TMTT Oct. 2012 3023-3034 Design and Analysis of a Tri-Band Dual-Mode Chip Filter for 60-, 77-, and 100-GHz Applications. Yang, C.-L., +, TMTT April 2012 989-997 Design and Diagnosis of Wideband Coupled-Resonator Bandpass Filters. Lee, H.-M., +, TMTT May 2012 1266-1277 Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators. Ahn, H.-R., +, TMTT June 2012 1549-1559 Design Method for Ultra-Wideband Bandpass Filter With Wide Stopband Using Parallel-Coupled Microstrip Lines. Abbosh, A. M., +, TMTT Jan. 2012 31-38 Design of High-Order Wideband Planar Balun Filter in -Plane Bandpass Prototype. Lin, Y.-W., +, TMTT July 2012 2124-2130 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Dual-Mode Ring Resonator Bandpass Filter With Asymmetric Inductive Coupling and Its Miniaturization. Lin, T.-W., +, TMTT Sept. 2012 28082814 + Check author entry for coauthors

Extended Passband Bandstop Filter Cascade With Continuous 0.85–6.6-GHz Coverage. Naglich, E. J., +, TMTT Jan. 2012 21-30 Extremely Miniaturized Bandpass Filters Based on Asymmetric Coupled Lines With Equal Reactance. Park, J.-H., +, TMTT Feb. 2012 261-269 Harmonic Suppressed Dual-Band Bandpass Filters With Tunable Passbands. Chaudhary, G., +, TMTT July 2012 2115-2123 Highly Miniaturized Multiband Bandpass Filter Design Based on a Stacked Spiral Resonator Structure. Chen, C.-H., +, TMTT May 2012 1278-1286 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Microstrip Bandpass Filters With Various Resonators Using Connected- and Edge-Coupling Mechanisms and Their Applications to Dual-Band Filters and Diplexers. Lin, S.-C., +, TMTT April 2012 975-988 Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology. Qian, S., +, TMTT Sept. 2012 2799-2807 Miniaturized UWB Filters Integrated With Tunable Notch Filters Using a Silicon-Based Integrated Passive Device Technology. Wu, Z., +, TMTT March 2012 518-527 Multilayer Antenna-Filter Antenna for Beam-Steering Transmit-Array Applications. Boccia, L., +, TMTT July 2012 2287-2300 Novel Wideband Differential Bandpass Filters Based on T-Shaped Structure. Feng, W., +, TMTT June 2012 1560-1568 Power Handling of Electrostatic MEMS Evanescent-Mode (EVA) Tunable Bandpass Filters. Liu, X., +, TMTT Feb. 2012 270-283 Stepped-Impedance Coupled Resonators for Implementation of Parallel Coupled Microstrip Filters With Spurious Band Suppression. Worapishet, A., +, TMTT June 2012 1540-1548 Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control. Serrano, A. L. C., +, TMTT March 2012 484-493 Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay. Zhang, Q., +, TMTT Aug. 2012 2394-2402 Unequal Wilkinson Power Dividers With Favorable Selectivity and HighIsolation Using Coupled-Line Filter Transformers. Deng, P.-H., +, TMTT June 2012 1520-1529 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Band-stop filters Design Method for Ultra-Wideband Bandpass Filter With Wide Stopband Using Parallel-Coupled Microstrip Lines. Abbosh, A. M., +, TMTT Jan. 2012 31-38 Design of High-Order Wideband Planar Balun Filter in -Plane Bandpass Prototype. Lin, Y.-W., +, TMTT July 2012 2124-2130 Lumped-Element Realization of Absorptive Bandstop Filter With Anomalously High Spectral Isolation. Lee, J., +, TMTT Aug. 2012 2424-2430 Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology. Qian, S., +, TMTT Sept. 2012 2799-2807 Switchless Tunable Bandstop-to-All-Pass Reconfigurable Filter. Naglich, E. J., +, TMTT May 2012 1258-1265 Bandwidth A 64–84-GHz PLL With Low Phase Noise in an 80-GHz SiGe HBT Technology. Liu, G., +, TMTT Dec. 2012 3739-3748 A Modified Doherty Configuration for Broadband Amplification Using Symmetrical Devices. Wu, D. Y.-T., +, TMTT Oct. 2012 3201-3213 Analog Signal Processing for Pulse Compression Radar in 90-nm CMOS. Parlak, M., +, TMTT Dec. 2012 3810-3822 CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution. Gupta, S., +, TMTT Dec. 2012 3939-3949 Design and Analysis of Digital-Assisted Bandwidth-Enhanced Miller Divider in 0.18- m CMOS Process. Kuo, Y.-H., +, TMTT Dec. 2012 37693777 Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier F Mode Transferring. Chen, K., +, Using In-Band Continuous Class-F TMTT Dec. 2012 4107-4116 Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines. Sun, J. S., +, TMTT Dec. 2012 3950-3958 Sensitivity of a Passive Correlation Interferometer to an Angularly Moving Source. Nanzer, J. A., +, TMTT Dec. 2012 3868-3876

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Barium compounds A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 Baseband Analog Signal Processing for Pulse Compression Radar in 90-nm CMOS. Parlak, M., +, TMTT Dec. 2012 3810-3822 Beam steering 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 Multilayer Antenna-Filter Antenna for Beam-Steering Transmit-Array Applications. Boccia, L., +, TMTT July 2012 2287-2300 Optical Modulation of Millimeter-Wave Beams Using a Semiconductor Substrate. Gallacher, T. F., +, TMTT July 2012 2301-2309 Pseudo-Traveling-Wave Resonator With Magnetically Tunable Phase Gradient of Fields and Its Applications to Beam-Steering Antennas. Ueda, T., +, TMTT Oct. 2012 3043-3054 Bessel functions Efficient Analysis of Substrate Integrated Waveguide Devices Using Hybrid Mode Matching Between Cylindrical and Guided Modes. Diaz Caballero, E., +, TMTT Feb. 2012 232-243 Hybrid Field/Transmission-Line Model for the Study of Coaxial Corrugated Waveguides. Savaidis, S. P., +, TMTT Oct. 2012 2972-2978 BiCMOS analogue integrated circuits 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490 A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Analysis and Design of a Stacked Power Amplifier With Very High Bandwidth. Fritsche, D., +, TMTT Oct. 2012 3223-3231 BiCMOS integrated circuits A 1.1-V Regulator-Stabilized 21.4-GHz VCO and a 115% Frequency-Range Dynamic Divider for -Band Wireless Communication. Nakamura, T., +, TMTT Sept. 2012 2823-2832 A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array. Kim, C.-Y., +, TMTT March 2012 730-742 A 5-Gb/s 2.1–2.2-GHz Bandpass Modulator for Switch-Mode Power Amplifier. Ostrovskyy, P., +, TMTT Aug. 2012 2524-2531 A Nested-Reactance Feedback Power Amplifier for -Band Applications. Kalantari, N., +, TMTT June 2012 1667-1675 A Transformer-Coupling Current-Reuse SiGe HBT Power Amplifier for 77-GHz Automotive Radar. Giammello, V., +, TMTT June 2012 1676-1683 An Improved Wideband All-Pass I/Q Network for Millimeter-Wave Phase Shifters. Kim, S. Y., +, TMTT Nov. 2012 3431-3439 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Design and Analysis of a Low-Power 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance. Uzunkol, M., +, TMTT Oct. 2012 32633271 Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators. Gupta, A. K., +, TMTT Oct. 2012 3272-3285 Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Bifurcation Analysis of Oscillation Modes in Free-Running Ring Oscillators. de Cos, J., +, TMTT Oct. 2012 3137-3150 Analysis of the Locking Range of Rationally Synchronized Oscillators With High Reference Signal Power. Fernandez Garcia, M., +, TMTT Aug. 2012 2494-2504 Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes. Suarez, A., +, TMTT March 2012 528-541 Bioelectric phenomena Frequency Multiplexed 2-Dimensional Sensor Array Based on Split-Ring Resonators for Organic Tissue Analysis. Puentes, M., +, TMTT June 2012 1720-1727 + Check author entry for coauthors

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The Signal Transmission Mechanism on the Surface of Human Body for Body Channel Communication. Bae, J., +, TMTT March 2012 582-593 Biological effects of fields Mechanisms of RF Electromagnetic Field Absorption in Human Hands and Fingers. Li, C.-H., +, TMTT July 2012 2267-2276 The Signal Transmission Mechanism on the Surface of Human Body for Body Channel Communication. Bae, J., +, TMTT March 2012 582-593 Biological effects of microwaves In Vitro Dosimetry and Temperature Evaluations of a Typical MillimeterWave Aperture-Field Exposure Setup. Zhao, J., +, TMTT Nov. 2012 36083622 Biological effects of optical radiation Ear Temperature Increase Produced by Cellular Phones Under Extreme Exposure Conditions. De Santis, V., +, TMTT June 2012 1728-1734 Biological tissues Frequency Multiplexed 2-Dimensional Sensor Array Based on Split-Ring Resonators for Organic Tissue Analysis. Puentes, M., +, TMTT June 2012 1720-1727 Biomedical electronics Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Biomedical equipment Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Biomedical measurement Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Biosensors Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Frequency Multiplexed 2-Dimensional Sensor Array Based on Split-Ring Resonators for Organic Tissue Analysis. Puentes, M., +, TMTT June 2012 1720-1727 Bipolar MIMIC A Nested-Reactance Feedback Power Amplifier for -Band Applications. Kalantari, N., +, TMTT June 2012 1667-1675 A Transformer-Coupling Current-Reuse SiGe HBT Power Amplifier for 77-GHz Automotive Radar. Giammello, V., +, TMTT June 2012 1676-1683 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Birefringence A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Bluetooth A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 Body area networks A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 New Method for Determining Dielectric Properties of Skin and Phantoms at Millimeter Waves Based on Heating Kinetics. Chahat, N., +, TMTT March 2012 827-832 The Signal Transmission Mechanism on the Surface of Human Body for Body Channel Communication. Bae, J., +, TMTT March 2012 582-593 Borosilicate glasses A High-Performance Continuously Tunable MEMS Bandpass Filter at 1 GHz. Shim, Y., +, TMTT Aug. 2012 2439-2447 Boundary integral equations A Generalized Multiple Scattering Method for Dense Vias With Axially Anisotropic Modes in an Arbitrarily Shaped Plate Pair. Zhang, Y.-J., +, TMTT July 2012 2035-2045 Bragg gratings A Narrow-Passband and Frequency-Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT May 2012 1287-1296 A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742

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Broadband antennas A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module. Suga, R., +, TMTT March 2012 640-646 An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications. Kim, S., +, TMTT Dec. 2012 4178-4186 Broadband CMOS Millimeter-Wave Frequency Multiplier With Vivaldi Antenna in 3-D Chip-Scale Packaging. Tripodi, L., +, TMTT Dec. 2012 37613768 Broadband Millimeter-Wave Single Balanced Mixer and Its Applications to Substrate Integrated Wireless Systems. Zhang, Z.-Y., +, TMTT March 2012 660-669 Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes. Rouvalis, E., +, TMTT March 2012 509-517 Broadband communication A Modified Doherty Configuration for Broadband Amplification Using Symmetrical Devices. Wu, D. Y.-T., +, TMTT Oct. 2012 3201-3213 Broadband CMOS Millimeter-Wave Frequency Multiplier With Vivaldi Antenna in 3-D Chip-Scale Packaging. Tripodi, L., +, TMTT Dec. 2012 37613768 Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier Using In-Band Continuous Class-F F Mode Transferring. Chen, K., +, TMTT Dec. 2012 4107-4116 Broadband networks 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 Built-in self test A Phased Array RFIC With Built-In Self-Test Capabilities. Inac, O., +, TMTT Jan. 2012 139-148 Buried object detection Buried Object Characterization Using Ultra-Wideband Ground Penetrating Radar. Li, L., +, TMTT Aug. 2012 2654-2664 Butterworth filters Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators. Ahn, H.-R., +, TMTT June 2012 1549-1559

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Calibration 16-Term Error Model in Reciprocal Systems. Silvonen, K., +, TMTT Nov. 2012 3551-3558 A Compact 3-D Harmonic Repeater for Passive Wireless Sensing. Nassar, I. T., +, TMTT Oct. 2012 3309-3316 A Unified Theory for -Parameter Uncertainty Evaluation. Garelli, M., +, TMTT Dec. 2012 3844-3855 Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range. Voinigescu, S. P., +, TMTT Dec. 2012 4024-4034 Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467 Design and Analysis of an Ultra-Wideband Automatic Self-Calibrating Upconverter in 65-nm CMOS. Kang, B., +, TMTT July 2012 2178-2191 Design and Analysis of Digital-Assisted Bandwidth-Enhanced Miller Divider in 0.18- m CMOS Process. Kuo, Y.-H., +, TMTT Dec. 2012 37693777 Direct Baseband I-Q Regeneration Method for Five-Port Receivers Improving DC-Offset and Second-Order Intermodulation Distortion Rejection. de la Morena-Alvarez-Palencia, C., +, TMTT Aug. 2012 2634-2643 Experimental Characterization of Oscillator Circuits for Reduced-Order Models. Umpierrez, P., +, TMTT Nov. 2012 3527-3541 Formulation for Complete and Accurate Calibration of Six-Port Reflectometer. Haddadi, K., +, TMTT March 2012 574-581 Generalization and Reduction of Line-Series-Shunt Calibration for Broadband GaAs and CMOS On-Wafer Scattering Parameter Measurements. Huang, C.-C., +, TMTT Dec. 2012 4138-4144 Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators. Gupta, A. K., +, TMTT Oct. 2012 3272-3285 Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 + Check author entry for coauthors

Novel Modeling and Calibration Approach for Multiport Receivers Mitigating System Imperfections and Hardware Impairments. Hasan, A., +, TMTT Aug. 2012 2644-2653 Simulation and Measurement of the -Parameters of Obstacles in Periodic Waveguides. Navarro-Tapia, M., +, TMTT April 2012 1146-1155 Cameras Development of Optically Transparent Ultrathin Microwave Absorber for Ultrahigh-Frequency RF Identification System. Okano, Y., +, TMTT Aug. 2012 2456-2464 Capacitance A 1–8-GHz Miniaturized Spectroscopy System for Permittivity Detection and Mixture Characterization of Organic Chemicals. Helmy, A. A., +, TMTT Dec. 2012 4157-4170 A Physics-Based Causal Bond-Wire Model for RF Applications. Nazarian, A. L., +, TMTT Dec. 2012 3683-3692 Accurate Nanoliter Liquid Characterization Up to 40 GHz for Biomedical Applications: Toward Noninvasive Living Cells Monitoring. Chen, T., +, TMTT Dec. 2012 4171-4177 Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range. Voinigescu, S. P., +, TMTT Dec. 2012 4024-4034 Experimental Characterization of Stability Margins in Microwave Amplifiers. Otegi, N., +, TMTT Dec. 2012 4145-4156 On the Compression and Blocking Distortion of Semiconductor-Based Varactors. Huang, C., +, TMTT Dec. 2012 3699-3709 Capacitor switching A 50-Mb/s CMOS QPSK/O-QPSK Transmitter Employing Injection Locking for Direct Modulation. Diao, S., +, TMTT Jan. 2012 120-130 Capacitors A -Band Capacitor-Coupled QVCO Using Sinusoidal Current Bias Technique. Shen, I.-S., +, TMTT Feb. 2012 318-328 A 1–8-GHz Miniaturized Spectroscopy System for Permittivity Detection and Mixture Characterization of Organic Chemicals. Helmy, A. A., +, TMTT Dec. 2012 4157-4170 A Nonlinear Lattice for High-Amplitude Picosecond Pulse Generation in CMOS. Lee, W., +, TMTT Feb. 2012 370-380 Behaviors of Class-F and Class-F Amplifiers. Moon, J., +, TMTT June 2012 1937-1951 Design and Analysis of a Tri-Band Dual-Mode Chip Filter for 60-, 77-, and 100-GHz Applications. Yang, C.-L., +, TMTT April 2012 989-997 Design and Diagnosis of Wideband Coupled-Resonator Bandpass Filters. Lee, H.-M., +, TMTT May 2012 1266-1277 Design of High-Order Wideband Planar Balun Filter in -Plane Bandpass Prototype. Lin, Y.-W., +, TMTT July 2012 2124-2130 High-Quality-Factor Active Capacitors for Millimeter-Wave Applications. Ghadiri, A., +, TMTT Dec. 2012 3710-3718 Carbon nanotube field effect transistors Conformal Ink-Jet Printed -Band Phased-Array Antenna Incorporating Carbon Nanotube Field-Effect Transistor Based Reconfigurable True-Time Delay Lines. Chen, M. Y., +, TMTT Jan. 2012 179-184 Cardiology Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Cavity resonator filters Substrate Integrated Waveguide Quasi-Elliptic Filters With Controllable Electric and Magnetic Mixed Coupling. Gong, K., +, TMTT Oct. 2012 3071-3078 Cavity resonators A -Band Fully Tunable Cavity Filter. Yassini, B., +, TMTT Dec. 2012 4002-4012 Inline Pseudoelliptic -Mode Dielectric Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Orthogonal Resonators. Bastioli, S., +, TMTT Dec. 2012 3988-4001 Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity. Ruiz-Cruz, J. A., +, TMTT Dec. 2012 3969-3979 Widely Tunable High-Efficiency Power Amplifier With Ultra-Narrow Instantaneous Bandwidth. Chen, K., +, TMTT Dec. 2012 3787-3797 Ceramic packaging A Fully SiP Integrated -Band Butler Matrix End-Fire Beam-Switching Transmitter Using Flip-Chip Assembled CMOS Chips on LTCC. Kuo, C.-C., +, TMTT May 2012 1424-1436 Synthesis of Vertical Interdigital Filters Using Multilayered Technologies. Perigaud, A., +, TMTT April 2012 965-974

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Ceramics 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 Channel bank filters Intrinsically Switched Varactor-Tuned Filters and Filter Banks. Guyette, A. C., +, TMTT April 2012 1044-1056 Chaos Variability Analysis of Multiport Systems Via Polynomial-Chaos Expansion. Spina, D., +, TMTT Aug. 2012 2329-2338 Chebyshev approximation Complex-Chebyshev Functional Link Neural Network Behavioral Model for Broadband Wireless Power Amplifiers. Li, M., +, TMTT June 2012 1979-1989 Chebyshev filters A Temperature-Compensation Technique for Substrate Integrated Waveguide Cavities and Filters. Djerafi, T., +, TMTT Aug. 2012 2448-2455 Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators. Ahn, H.-R., +, TMTT June 2012 1549-1559 On the Relation Between Stored Energy and Fabrication Tolerances in Microwave Filters. Martinez-Mendoza, M., +, TMTT July 2012 2131-2141 Phase Velocities Equalization of Coupled Microstrip Lines Using -Shaped Particles and Suppression of the Second Harmonic. Hatefi Ardakani, H., +, TMTT March 2012 464-470 Stepped-Impedance Coupled Resonators for Implementation of Parallel Coupled Microstrip Filters With Spurious Band Suppression. Worapishet, A., +, TMTT June 2012 1540-1548 Chemical sensors Microwave Chemical Sensing at Room Temperature Using an Overmoded Waveguide Design. Huang, Y.-T., +, TMTT Sept. 2012 2886-2893 Chirality Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies. Bayatpur, F., +, TMTT April 2012 1126-1135 Circuit CAD Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828 Circuit complexity An Equivalent Circuit for Discontinuities Exciting Evanescent Accessible Modes. Zappelli, L., +, TMTT May 2012 1197-1209 Design of a New Type Planar Balun by Using Trans-Directional Couplers. Shie, C.-I., +, TMTT March 2012 471-476 Circuit feedback A Nested-Reactance Feedback Power Amplifier for -Band Applications. Kalantari, N., +, TMTT June 2012 1667-1675 Millimeter-Wave Self-Healing Power Amplifier With Adaptive Amplitude and Phase Linearization in 65-nm CMOS. Liu, J. Y.-C., +, TMTT May 2012 1342-1352 Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Circuit noise Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078 Circuit optimization Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Circuit simulation New Trends for the Nonlinear Measurement and Modeling of High-Power RF Transistors and Amplifiers With Memory Effects. Roblin, P., +, TMTT June 2012 1964-1978 Passivity Enforcement for Admittance Models of Distributed Networks Using an Inverse Eigenvalue Method. Saunders, C. S., +, TMTT Jan. 2012 8-20 Robust Passive Macro-Model Generation With Local Compensation. Wang, T., +, TMTT Aug. 2012 2313-2328 Circuit stability A Broadband Injection-Locking Class-E Power Amplifier. Lin, C.-H., +, TMTT Oct. 2012 3232-3242 Analysis of Oscillation Modes in Free-Running Ring Oscillators. de Cos, J., +, TMTT Oct. 2012 3137-3150 Experimental Characterization of Stability Margins in Microwave Amplifiers. Otegi, N., +, TMTT Dec. 2012 4145-4156

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Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes. Suarez, A., +, TMTT March 2012 528-541 Circuit tuning A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Intrinsically Switched Varactor-Tuned Filters and Filter Banks. Guyette, A. C., +, TMTT April 2012 1044-1056 Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078 Circular waveguides A Systematic Design Procedure of Classical Dual-Mode Circular Waveguide Filters Using an Equivalent Distributed Model. Cogollos, S., +, TMTT April 2012 1006-1017 Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network. Penaranda-Foix, F. L., +, TMTT Sept. 2012 2730-2740 Gyrotropy and Nonreciprocity of Graphene for Microwave Applications. Sounas, D. L., +, TMTT April 2012 901-914 Circulators A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the Turnstile Waveguide Circulator. Helszajn, J., +, TMTT Oct. 2012 3079-3087 CMOS analog integrated circuits 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 A 130-nm CMOS 100-Hz–6-GHz Reconfigurable Vector Signal Analyzer and Software-Defined Receiver. Goel, A., +, TMTT May 2012 1375-1389 A 50-Mb/s CMOS QPSK/O-QPSK Transmitter Employing Injection Locking for Direct Modulation. Diao, S., +, TMTT Jan. 2012 120-130 A CMOS Noise-Squeezing Amplifier. Lee, W., +, TMTT Feb. 2012 329-339 A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications. Son, K. Y., +, TMTT Aug. 2012 2571-2580 A Fully Integrated Adaptive Multiband Multimode Switching-Mode CMOS Power Amplifier. Aref, A. F., +, TMTT Aug. 2012 2549-2561 A Highly Linear and Efficient CMOS RF Power Amplifier With a 2-D Circuit Synthesis Technique. Ding, M., +, TMTT Sept. 2012 2851-2862 A Precise Decibel-Linear Programmable Gain Amplifier Using a Constant Current-Density Function. Kang, S.-Y., +, TMTT Sept. 2012 2843-2850 A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications. Hassan, M., +, TMTT May 2012 1321-1330 A Wideband Low-Power CMOS LNA With Positive–Negative Feedback for Noise, Gain, and Linearity Optimization. Woo, S., +, TMTT Oct. 2012 3169-3178 All-Digital RF Modulator. Alavi, M. S., +, TMTT Nov. 2012 3513-3526 An Ultra-Compact, Linearly-Controlled Variable Phase Shifter Designed With a Novel RC Poly-Phase Filter. Huang, Y.-Y., +, TMTT Feb. 2012 301-310 Design of CMOS Power Amplifiers. Niknejad, A. M., +, TMTT June 2012 1784-1796 Design-in-Reliable Millimeter-Wave Power Amplifiers in a 65-nm CMOS Process. Quemerais, T., +, TMTT April 2012 1079-1085 ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process. Lin, C.-Y., +, TMTT March 2012 714-723 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 Integrated Bias Circuits of RF CMOS Cascode Power Amplifier for Linearity Enhancement. Koo, B., +, TMTT Feb. 2012 340-351 Millimeter-Wave Self-Healing Power Amplifier With Adaptive Amplitude and Phase Linearization in 65-nm CMOS. Liu, J. Y.-C., +, TMTT May 2012 1342-1352 Two-Way Current-Combining -Band Power Amplifier in 65-nm CMOS. Gu, Q. J., +, TMTT May 2012 1365-1374 Wideband CMOS Amplification Stage for a Direct-Sampling Square Kilometre Array Receiver. Navaratne, D., +, TMTT Oct. 2012 3179-3188 Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078

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CMOS integrated circuits -Band CMOS Differential and Quadrature Voltage-Controlled Oscillators for Low Phase-Noise and Low-Power Applications. Chang, H.-Y., +, TMTT Jan. 2012 46-59 -Band and -Band Power Amplifiers in 45-nm CMOS SOI. Kim, J., +, TMTT June 2012 1870-1877 -Band Amplifiers With 6-dB Noise Figure and Milliwatt-Level 170–200-GHz Doublers in 45-nm CMOS. Cetinoneri, B., +, TMTT March 2012 692-701 0.6–3-GHz Wideband Receiver RF Front-End With a Feedforward Noise and Distortion Cancellation Resistive-Feedback LNA. Wang, X., +, TMTT Feb. 2012 387-392 60-GHz Dual-Conversion Down-/Up-Converters Using Schottky Diode in 0.18 m Foundry CMOS Technology. Wei, H.-J., +, TMTT June 2012 16841698 A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer. Tang, A., +, TMTT Dec. 2012 4129-4137 A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator. Lee, S., +, TMTT May 2012 1405-1412 A 0.01–8-GHz (12.5 Gb/s) 4 4 CMOS Switch Matrix. Shin, D., +, TMTT Feb. 2012 381-386 A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 A 24-GHz CMOS UWB Radar Transmitter With Compressed Pulses. Yang, J., +, TMTT April 2012 1117-1125 A 30.8-dBm Wideband CMOS Power Amplifier With Minimized Supply Fluctuation. Jin, B., +, TMTT June 2012 1658-1666 A CMOS Distributed Amplifier With Distributed Active Input Balun Using GBW and Linearity Enhancing Techniques. Jahanian, A., +, TMTT May 2012 1331-1341 A Digital-Intensive Multimode Multiband Receiver Using a Sinc FilterEmbedded VCO-Based ADC. Kim, J., +, TMTT Oct. 2012 3254-3262 A Dual-Band 10/24-GHz Amplifier Design Incorporating Dual-Frequency Complex Load Matching. Hsieh, K.-A., +, TMTT June 2012 1649-1657 A Dual-Resonant Mode 10/22-GHz VCO With a Novel Inductive Switching Approach. Liu, S.-L., +, TMTT July 2012 2165-2177 A Full 360 Vector-Sum Phase Shifter With Very Low RMS Phase Error Over a Wide Bandwidth. Asoodeh, A., +, TMTT June 2012 1626-1634 A Fully Integrated 0.18- m CMOS Transceiver Chip for -Band PhasedArray Systems. Gharibdoust, K., +, TMTT July 2012 2192-2202 A Fully Integrated Watt-Level Linear 900-MHz CMOS RF Power Amplifier for LTE-Applications. Francois, B., +, TMTT June 2012 1878-1885 A Fully SiP Integrated -Band Butler Matrix End-Fire Beam-Switching Transmitter Using Flip-Chip Assembled CMOS Chips on LTCC. Kuo, C.-C., +, TMTT May 2012 1424-1436 A High Dynamic-Range RF Programmable-Gain Front End for G.hn RF-Coax in 65-nm CMOS. Trulls, X., +, TMTT Oct. 2012 3243-3253 A Highly Reconfigurable Low-Power CMOS Directional Coupler. Sun, J., +, TMTT Sept. 2012 2815-2822 A Low-Voltage, Low-Power, and Low-Noise UWB Mixer Using Bulk-Injection and Switched Biasing Techniques. Kim, M.-G., +, TMTT Aug. 2012 2486-2493 A Narrowband CMOS Ring Resonator Dual-Mode Active Bandpass Filter With Edge Periphery of 2% Free-Space Wavelength. Su, L., +, TMTT June 2012 1605-1616 A Nonlinear Lattice for High-Amplitude Picosecond Pulse Generation in CMOS. Lee, W., +, TMTT Feb. 2012 370-380 A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 A Waveform-Dependent Phase-Noise Analysis for Edge-Combining DLL Frequency Multipliers. Liao, F.-R., +, TMTT April 2012 1086-1096 A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN. Chen, J.-H., +, TMTT Dec. 2012 4089-4096 An Improved Wideband All-Pass I/Q Network for Millimeter-Wave Phase Shifters. Kim, S. Y., +, TMTT Nov. 2012 3431-3439 An Open-Loop Half-Quadrature Hybrid for Multiphase Signals Generation. Chen, H.-S., +, TMTT Jan. 2012 131-138 An Ultra-Low-Voltage and Low-Power 2 Subharmonic Downconverter Mixer. He, S., +, TMTT Feb. 2012 311-317 Analysis and Design of 60-GHz SPDT Switch in 130-nm CMOS. He, J., +, TMTT Oct. 2012 3113-3119 Analysis and Design of a 60 GHz Wideband Voltage-Voltage Transformer Feedback LNA. Sakian, P., +, TMTT March 2012 702-713 + Check author entry for coauthors

Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique. Yeh, H.-C., +, TMTT Dec. 2012 4066-4079 Analysis of a New 33–58-GHz Doubly Balanced Drain Mixer in 90-nm CMOS Technology. Yang, H.-Y., +, TMTT April 2012 1057-1068 Broadband CMOS Millimeter-Wave Frequency Multiplier With Vivaldi Antenna in 3-D Chip-Scale Packaging. Tripodi, L., +, TMTT Dec. 2012 37613768 Compact Wideband Linear CMOS Variable Gain Amplifier for Analog-Predistortion Power Amplifiers. Huang, Y.-Y., +, TMTT Jan. 2012 68-76 Design and Analysis of a -band Divide-by-Three Injection-Locked Frequency Divider Using Second Harmonic Enhancement Technique. Yeh, Y.-L., +, TMTT June 2012 1617-1625 Design and Analysis of a 21–29-GHz Ultra-Wideband Receiver Front-End in 0.18- m CMOS Technology. Lin, Y.-S., +, TMTT Aug. 2012 2590-2604 Design and Analysis of an Ultra-Wideband Automatic Self-Calibrating Upconverter in 65-nm CMOS. Kang, B., +, TMTT July 2012 2178-2191 Design and Analysis of Down-Conversion Gate/Base-Pumped Harmonic Mixers Using Novel Reduced-Size 180 Hybrid With Different Input Frequencies. Kuo, J.-J., +, TMTT Aug. 2012 2473-2485 Design of 40–108-GHz Low-Power and High-Speed CMOS Up-/DownConversion Ring Mixers for Multistandard MMW Radio Applications. Tsai, J.-H., +, TMTT March 2012 670-678 Generalization and Reduction of Line-Series-Shunt Calibration for Broadband GaAs and CMOS On-Wafer Scattering Parameter Measurements. Huang, C.-C., +, TMTT Dec. 2012 4138-4144 Guest Editorial. Rebeiz, G. M., +, TMTT March 2012 637-639 High-Efficiency Cellular Power Amplifiers Based on a Modified LDMOS Process on Bulk Silicon and Silicon-On-Insulator Substrates With Integrated Power Management Circuitry. Tombak, A., +, TMTT June 2012 1862-1869 High-Quality-Factor Active Capacitors for Millimeter-Wave Applications. Ghadiri, A., +, TMTT Dec. 2012 3710-3718 Investigation of Wideband Load Transformation Networks for Class-E Switching-Mode Power Amplifiers. Wei, M.-D., +, TMTT June 2012 1916-1927 Low-Power Sub-Harmonic Direct-Conversion Receiver With Tunable RF LNA and Wideband LO Generator at U-NII Bands. Syu, J.-S., +, TMTT March 2012 555-566 Low-Voltage -Band Divide-by-3 Injection-Locked Frequency Divider With Floating-Source Differential Injector. Chen, Y.-T., +, TMTT Jan. 2012 60-67 Low-Voltage, Wide-Locking-Range, Millimeter-Wave Divide-by-5 Injection-Locked Frequency Dividers. Li, M.-W., +, TMTT March 2012 679-685 Modeling and Digital Predistortion of Class-D Outphasing RF Power Amplifiers. Landin, P. N., +, TMTT June 2012 1907-1915 Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation. Jooyaie, A., +, TMTT Aug. 2012 2505-2511 Parasitic-Insensitive Linearization Methods for 60-GHz 90-nm CMOS LNAs. Li, W.-T., +, TMTT Aug. 2012 2512-2523 Pulse-Biased Low-Power Low-Phase-Noise UHF LC-QVCO for 866 MHz RFID Front-End. Li, J., +, TMTT Oct. 2012 3120-3125 Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems. Thomas, S. J., +, TMTT April 2012 1175-1182 Reconfigurable Dual-Channel Multiband RF Receiver for GPS/ Galileo/BD-2 Systems. Chen, D., +, TMTT Nov. 2012 3491-3501 Theoretical Analysis and Practical Considerations for the Integrated TimeStretching System Using Dispersive Delay Line (DDL). Xiang, B., +, TMTT Nov. 2012 3449-3457 CMOS process High-Quality-Factor Active Capacitors for Millimeter-Wave Applications. Ghadiri, A., +, TMTT Dec. 2012 3710-3718 CMOS technology A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN. Chen, J.-H., +, TMTT Dec. 2012 4089-4096 Coaxial cables Novel Coupling Structure for the Resonant Coaxial Probe. Rowe, D. J., +, TMTT June 2012 1699-1708 Ultra-Wideband Single and Dual Baluns Based on Substrate Integrated Coaxial Line Technology. Zhu, F., +, TMTT Oct. 2012 3062-3070 Coaxial waveguides Design of a Broadband Eight-Way Coaxial Waveguide Power Combiner. Amjadi, M., +, TMTT Jan. 2012 39-45

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network. Penaranda-Foix, F. L., +, TMTT Sept. 2012 2730-2740 Hybrid Field/Transmission-Line Model for the Study of Coaxial Corrugated Waveguides. Savaidis, S. P., +, TMTT Oct. 2012 2972-2978 Ultra-Wideband Single and Dual Baluns Based on Substrate Integrated Coaxial Line Technology. Zhu, F., +, TMTT Oct. 2012 3062-3070 Cobalt compounds 60-GHz Dual-Conversion Down-/Up-Converters Using Schottky Diode in 0.18 m Foundry CMOS Technology. Wei, H.-J., +, TMTT June 2012 16841698 Code division multiple access Modulator for Switch-Mode Power A 5-Gb/s 2.1–2.2-GHz Bandpass Amplifier. Ostrovskyy, P., +, TMTT Aug. 2012 2524-2531 A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications. Son, K. Y., +, TMTT Aug. 2012 2571-2580 A Dual-Band Parallel Doherty Power Amplifier for Wireless Applications. Grebennikov, A., +, TMTT Oct. 2012 3214-3222 A Simplified Broadband Design Methodology for Linearized High-Efficiency Continuous Class-F Power Amplifiers. Tuffy, N., +, TMTT June 2012 1952-1963 A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 Closed-Loop Digital Predistortion System With Fast Real-Time Adaptation Applied to a Handset WCDMA PA Module. Presti, C. D., +, TMTT March 2012 604-618 Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters. Hoversten, J., +, TMTT June 2012 2010-2020 Complex-Chebyshev Functional Link Neural Network Behavioral Model for Broadband Wireless Power Amplifiers. Li, M., +, TMTT June 2012 1979-1989 Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 Digital Predistortion Using a Vector-Switched Model. Afsardoost, S., +, TMTT April 2012 1166-1174 Modeling and Digital Predistortion of Class-D Outphasing RF Power Amplifiers. Landin, P. N., +, TMTT June 2012 1907-1915 Novel Modeling and Calibration Approach for Multiport Receivers Mitigating System Imperfections and Hardware Impairments. Hasan, A., +, TMTT Aug. 2012 2644-2653 Single-Chip Multiband EGPRS and SAW-Less LTE WCDMA CMOS Receiver With Diversity. Xie, H., +, TMTT May 2012 1390-1396 Cognitive radio A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 Comb filters A Quasi Elliptic Function 1.75–2.25 GHz 3-Pole Bandpass Filter With Bandwidth Control. Chiou, Y.-C., +, TMTT Feb. 2012 244-249 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Communication complexity Digital Predistortion Using a Vector-Switched Model. Afsardoost, S., +, TMTT April 2012 1166-1174 Compensation A Precise Decibel-Linear Programmable Gain Amplifier Using a Constant Current-Density Function. Kang, S.-Y., +, TMTT Sept. 2012 2843-2850 Millimeter-Wave Self-Healing Power Amplifier With Adaptive Amplitude and Phase Linearization in 65-nm CMOS. Liu, J. Y.-C., +, TMTT May 2012 1342-1352 Composite materials Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 Computational complexity An Instrumental Variable Vector-Fitting Approach for Noisy Frequency Responses. Beygi, A., +, TMTT Sept. 2012 2702-2712 Complex-Chebyshev Functional Link Neural Network Behavioral Model for Broadband Wireless Power Amplifiers. Li, M., +, TMTT June 2012 1979-1989

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Optimized Low-Complexity Implementation of Least Squares Based Model Extraction for Digital Predistortion of RF Power Amplifiers. Guan, L., +, TMTT March 2012 594-603 Computational modeling Multiphysics Modeling of RF and Microwave High-Power Transistors. Aaen, P. H., +, TMTT Dec. 2012 4013-4023 Conductors Coupled Line 180 Hybrids With Lange Couplers. Napijalo, V., +, TMTT Dec. 2012 3674-3682 Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity. Ruiz-Cruz, J. A., +, TMTT Dec. 2012 3969-3979 Conjugate gradient methods MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit. De Donno, D., +, TMTT Sept. 2012 2693-2701 Convergence An Instrumental Variable Vector-Fitting Approach for Noisy Frequency Responses. Beygi, A., +, TMTT Sept. 2012 2702-2712 Convergence of numerical methods Robust Passive Macro-Model Generation With Local Compensation. Wang, T., +, TMTT Aug. 2012 2313-2328 Convex programming Peak-Power Controlled Digital Predistorters for RF Power Amplifiers. Landin, P. N., +, TMTT Nov. 2012 3582-3590 Cooling In Vitro Dosimetry and Temperature Evaluations of a Typical MillimeterWave Aperture-Field Exposure Setup. Zhao, J., +, TMTT Nov. 2012 36083622 Coplanar waveguides A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 Broadband CMOS Millimeter-Wave Frequency Multiplier With Vivaldi Antenna in 3-D Chip-Scale Packaging. Tripodi, L., +, TMTT Dec. 2012 37613768 Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes. Rouvalis, E., +, TMTT March 2012 509-517 Design of Compact and Auto-Compensated Single-Layer Chipless RFID Tag. Vena, A., +, TMTT Sept. 2012 2913-2924 Dual Composite Right-/Left-Handed Coplanar Waveguide Transmission Line Using Inductively Connected Split-Ring Resonators. Belenguer, A., +, TMTT Oct. 2012 3035-3042 Dual-Mode Ring Resonator Bandpass Filter With Asymmetric Inductive Coupling and Its Miniaturization. Lin, T.-W., +, TMTT Sept. 2012 28082814 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 Novel Second-Order Dual-Mode Dual-Band Filters Using Capacitance Loaded Square Loop Resonator. Fu, S., +, TMTT March 2012 477-483 Correlation Sensitivity of a Passive Correlation Interferometer to an Angularly Moving Source. Nanzer, J. A., +, TMTT Dec. 2012 3868-3876 Correlators Analog Signal Processing for Pulse Compression Radar in 90-nm CMOS. Parlak, M., +, TMTT Dec. 2012 3810-3822 Coupled circuits A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 A Systematic Design Procedure of Classical Dual-Mode Circular Waveguide Filters Using an Equivalent Distributed Model. Cogollos, S., +, TMTT April 2012 1006-1017 Power Amplification at 0.65 THz Using InP HEMTs. Radisic, V., +, TMTT March 2012 724-729 Coupled transmission lines A Directivity-Enhanced Directional Coupler Using Epsilon Negative Transmission Line. Pourzadi, A., +, TMTT Nov. 2012 3395-3402 Design of a New Type Planar Balun by Using Trans-Directional Couplers. Shie, C.-I., +, TMTT March 2012 471-476 Design of Compact Quad-Frequency Impedance Transformer Using TwoSection Coupled Line. Bai, Y.-F., +, TMTT Aug. 2012 2417-2423 Design of Transmission-Type th-Order Differentiators in Planar Microwave Technology. Chudzik, M., +, TMTT Nov. 2012 3384-3394 Experimental Validation of Frozen Modes Guided on Printed Coupled Transmission Lines. Apaydin, N., +, TMTT June 2012 1513-1519

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Generalized Lattice Network-Based Balanced Composite Right-/LeftHanded Transmission Lines. Esteban, J., +, TMTT Aug. 2012 2385-2393 Couplers Coupled Line 180 Hybrids With Lange Couplers. Napijalo, V., +, TMTT Dec. 2012 3674-3682 CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution. Gupta, S., +, TMTT Dec. 2012 3939-3949 Variable Reflection-Type Attenuators Based on Varactor Diodes. Bulja, S., +, TMTT Dec. 2012 3719-3727 Couplings -Band Fully Tunable Cavity Filter. Yassini, B., +, TMTT Dec. 2012 A 4002-4012 Coupled Line 180 Hybrids With Lange Couplers. Napijalo, V., +, TMTT Dec. 2012 3674-3682 CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution. Gupta, S., +, TMTT Dec. 2012 3939-3949 Inline Pseudoelliptic -Mode Dielectric Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Orthogonal Resonators. Bastioli, S., +, TMTT Dec. 2012 3988-4001 Narrowband Microwave Filters With Mixed Topology. Macchiarella, G., +, TMTT Dec. 2012 3980-3987 Novel Coupling Structure for the Resonant Coaxial Probe. Rowe, D. J., +, TMTT June 2012 1699-1708 Wideband Dual-Mode Microstrip Filter Using Short-Ended Resonator With Centrally Loaded Inductive Stub. Sun, S.-J., +, TMTT Dec. 2012 3667-3673 Crosstalk Crosstalk Reduction for Superconducting Microwave Resonator Arrays. Noroozian, O., +, TMTT May 2012 1235-1243 Cryogenics 4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers. Aja Abelan, B., +, TMTT Dec. 2012 4080-4088 Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467 Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 Crystal filters Lumped-Element Realization of Absorptive Bandstop Filter With Anomalously High Spectral Isolation. Lee, J., +, TMTT Aug. 2012 2424-2430 Crystal resonators A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Current density A Precise Decibel-Linear Programmable Gain Amplifier Using a Constant Current-Density Function. Kang, S.-Y., +, TMTT Sept. 2012 2843-2850 Current measurement A Novel Model for Implementation of Gamma Radiation Effects in GaAs HBTs. Zhang, J., +, TMTT Dec. 2012 3693-3698 Current mirrors Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Current-mode logic Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Curve fitting An Instrumental Variable Vector-Fitting Approach for Noisy Frequency Responses. Beygi, A., +, TMTT Sept. 2012 2702-2712 On the Equivalence Between the Maxwell-Garnett Mixing Rule and the Debye Relaxation Formula. Salski, B., +, TMTT Aug. 2012 2352-2358 CW radar A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar. Jahn, M., +, TMTT March 2012 861-869 A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading. Koswatta, R. V., +, TMTT Sept. 2012 2925-2933 An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer. Pohl, N., +, TMTT March 2012 757-765

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D DC-DC power converters GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion. Garcia, J. A., +, TMTT Dec. 2012 4220-4229 High-Efficiency Cellular Power Amplifiers Based on a Modified LDMOS Process on Bulk Silicon and Silicon-On-Insulator Substrates With Integrated Power Management Circuitry. Tombak, A., +, TMTT June 2012 1862-1869 Debye temperature On the Equivalence Between the Maxwell-Garnett Mixing Rule and the Debye Relaxation Formula. Salski, B., +, TMTT Aug. 2012 2352-2358 Defected ground structures Harmonic Suppressed Dual-Band Bandpass Filters With Tunable Passbands. Chaudhary, G., +, TMTT July 2012 2115-2123 Degradation A Novel Model for Implementation of Gamma Radiation Effects in GaAs HBTs. Zhang, J., +, TMTT Dec. 2012 3693-3698 Delay circuits A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator. Lee, S., +, TMTT May 2012 1405-1412 Delay lines A 2-D Electronically Steered Phased-Array Antenna With 2 2 Elements in LC Display Technology. Karabey, O. H., +, TMTT May 2012 1297-1306 Conformal Ink-Jet Printed -Band Phased-Array Antenna Incorporating Carbon Nanotube Field-Effect Transistor Based Reconfigurable True-Time Delay Lines. Chen, M. Y., +, TMTT Jan. 2012 179-184 Delay lock loops A Waveform-Dependent Phase-Noise Analysis for Edge-Combining DLL Frequency Multipliers. Liao, F.-R., +, TMTT April 2012 1086-1096 Delay-differential systems Interpolation-Based Parameterized Model Order Reduction of Delayed Systems. Ferranti, F., +, TMTT March 2012 431-440 Delays A Waveform-Dependent Phase-Noise Analysis for Edge-Combining DLL Frequency Multipliers. Liao, F.-R., +, TMTT April 2012 1086-1096 CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution. Gupta, S., +, TMTT Dec. 2012 3939-3949 Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay. Zhang, Q., +, TMTT Aug. 2012 2394-2402 Delta-sigma modulation A 5-Gb/s 2.1–2.2-GHz Bandpass Modulator for Switch-Mode Power Amplifier. Ostrovskyy, P., +, TMTT Aug. 2012 2524-2531 Demodulators Multi-Gb/s Analog Synchronous QPSK Demodulator With Phase-Noise Suppression. Ulusoy, A. ., +, TMTT Nov. 2012 3591-3598 Design A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array. Kim, C.-Y., +, TMTT March 2012 730-742 Approach to the Design of Asymmetric Coupled-Line Directional Couplers With the Maximum Achievable Impedance-Transformation Ratio. Wincza, K., +, TMTT May 2012 1218-1225 Detectors CMOS Integrated Antenna-Coupled Field-Effect Transistors for the Detection of Radiation From 0.2 to 4.3 THz. Boppel, S., +, TMTT Dec. 2012 3834-3843 Design and Analysis of Digital-Assisted Bandwidth-Enhanced Miller Divider in 0.18- m CMOS Process. Kuo, Y.-H., +, TMTT Dec. 2012 37693777 Dielectric hysteresis A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Dielectric liquids A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Dielectric materials Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT March 2012 405-418

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation. Kilic, E., +, TMTT May 2012 14371443 Dielectric properties Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network. Penaranda-Foix, F. L., +, TMTT Sept. 2012 2730-2740 Millimeter-Wave Printed Circuit Board Characterization Using Substrate Integrated Waveguide Resonators. Zelenchuk, D. E., +, TMTT Oct. 2012 3300-3308 New Method for Determining Dielectric Properties of Skin and Phantoms at Millimeter Waves Based on Heating Kinetics. Chahat, N., +, TMTT March 2012 827-832 Dielectric relaxation A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Dielectric resonator filters Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network. Penaranda-Foix, F. L., +, TMTT Sept. 2012 2730-2740 Dielectric resonators Frequency Multiplexed 2-Dimensional Sensor Array Based on Split-Ring Resonators for Organic Tissue Analysis. Puentes, M., +, TMTT June 2012 1720-1727 Dielectric waveguides Exact and Closed-Form Cutoff Wavenumbers of Elliptical Dielectric Waveguides. Zouros, G. P., +, TMTT Sept. 2012 2741-2751 Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation. Kilic, E., +, TMTT May 2012 14371443 Dielectric-loaded waveguides Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network. Penaranda-Foix, F. L., +, TMTT Sept. 2012 2730-2740 Dielectrics Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT Dec. 2012 3908-3918 Inline Pseudoelliptic -Mode Dielectric Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Orthogonal Resonators. Bastioli, S., +, TMTT Dec. 2012 3988-4001 Differential amplifiers -Band and -Band Power Amplifiers in 45-nm CMOS SOI. Kim, J., +, TMTT June 2012 1870-1877 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 Compact Wideband Linear CMOS Variable Gain Amplifier for Analog-Predistortion Power Amplifiers. Huang, Y.-Y., +, TMTT Jan. 2012 68-76 Integrated Bias Circuits of RF CMOS Cascode Power Amplifier for Linearity Enhancement. Koo, B., +, TMTT Feb. 2012 340-351 Diffraction Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings. Memarian, M., +, TMTT Dec. 2012 3893-3907 Diffraction gratings Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings. Memarian, M., +, TMTT Dec. 2012 3893-3907 Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT March 2012 405-418 Digital control A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490 A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications. Son, K. Y., +, TMTT Aug. 2012 2571-2580 Peak-Power Controlling Technique for Enhancing Digital Pre-Distortion of RF Power Amplifiers. Nader, C., +, TMTT Nov. 2012 3571-3581 Digital-analogue conversion All-Digital RF Modulator. Alavi, M. S., +, TMTT Nov. 2012 3513-3526 Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators. Gupta, A. K., +, TMTT Oct. 2012 3272-3285 Peak-Power Controlled Digital Predistorters for RF Power Amplifiers. Landin, P. N., +, TMTT Nov. 2012 3582-3590 Directional couplers A Highly Reconfigurable Low-Power CMOS Directional Coupler. Sun, J., +, TMTT Sept. 2012 2815-2822 + Check author entry for coauthors

4259

Approach to the Design of Asymmetric Coupled-Line Directional Couplers With the Maximum Achievable Impedance-Transformation Ratio. Wincza, K., +, TMTT May 2012 1218-1225 Design of a New Type Planar Balun by Using Trans-Directional Couplers. Shie, C.-I., +, TMTT March 2012 471-476 Simulation and Experiment of a Compact Wideband 90 Differential Phase Shifter. Sorn, M., +, TMTT March 2012 494-501 Directive antennas A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Dispersion CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution. Gupta, S., +, TMTT Dec. 2012 3939-3949 Experimental Validation of Frozen Modes Guided on Printed Coupled Transmission Lines. Apaydin, N., +, TMTT June 2012 1513-1519 Dispersive media Numerical Stability and Dispersion Analysis of the Precise-Integration Time-Domain Method in Lossy Media. Sun, G., +, TMTT Sept. 2012 2723-2729 Distance measurement A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Distortion 0.6–3-GHz Wideband Receiver RF Front-End With a Feedforward Noise and Distortion Cancellation Resistive-Feedback LNA. Wang, X., +, TMTT Feb. 2012 387-392 Closed-Loop Digital Predistortion System With Fast Real-Time Adaptation Applied to a Handset WCDMA PA Module. Presti, C. D., +, TMTT March 2012 604-618 On the Compression and Blocking Distortion of Semiconductor-Based Varactors. Huang, C., +, TMTT Dec. 2012 3699-3709 Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Distortion measurement Robust Analog Canceller for High-Dynamic-Range Radio Frequency Measurement. Wetherington, J. M., +, TMTT June 2012 1709-1719 Distributed amplifiers A CMOS Distributed Amplifier With Distributed Active Input Balun Using GBW and Linearity Enhancing Techniques. Jahanian, A., +, TMTT May 2012 1331-1341 Ring-Resonator-Inspired Power Recycling Scheme for Gain-Enhanced Distributed Amplifier-Based CRLH-Transmission Line Leaky Wave Antennas. Wu, C.-T. M., +, TMTT April 2012 1027-1037 Distributed databases Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach. Kabir, M., +, TMTT Dec. 2012 3927-3938 Diversity reception 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 Dosimetry In Vitro Dosimetry and Temperature Evaluations of a Typical MillimeterWave Aperture-Field Exposure Setup. Zhao, J., +, TMTT Nov. 2012 36083622 Drilling Localized Rapid Heating by Low-Power Solid-State Microwave Drill. Meir, Y., +, TMTT Aug. 2012 2665-2672 Driver circuits Localized Rapid Heating by Low-Power Solid-State Microwave Drill. Meir, Y., +, TMTT Aug. 2012 2665-2672 Dual band Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity. Ruiz-Cruz, J. A., +, TMTT Dec. 2012 3969-3979 E Ear protection Ear Temperature Increase Produced by Cellular Phones Under Extreme Exposure Conditions. De Santis, V., +, TMTT June 2012 1728-1734

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Earthing Crosstalk Reduction for Superconducting Microwave Resonator Arrays. Noroozian, O., +, TMTT May 2012 1235-1243 Eigenvalues and eigenfunctions A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the Turnstile Waveguide Circulator. Helszajn, J., +, TMTT Oct. 2012 3079-3087 A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide. Lee, J.-W., +, TMTT Dec. 2012 3642-3655 Analysis of Oscillation Modes in Free-Running Ring Oscillators. de Cos, J., +, TMTT Oct. 2012 3137-3150 Characterization of Waveguides With a Combination of Conductor and Periodic Boundary Contours: Application to the Analysis of Bi-Periodic Structures. Varela, J. E., +, TMTT March 2012 419-430 Finite-Element Eigenvalue Analysis of Propagating and Evanescent Modes in 3-D Periodic Structures Using Model-Order Reduction. Bostani, A., +, TMTT Sept. 2012 2677-2683 Passivity Enforcement for Admittance Models of Distributed Networks Using an Inverse Eigenvalue Method. Saunders, C. S., +, TMTT Jan. 2012 8-20 Electric admittance Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network. Penaranda-Foix, F. L., +, TMTT Sept. 2012 2730-2740 Passivity Enforcement for Admittance Models of Distributed Networks Using an Inverse Eigenvalue Method. Saunders, C. S., +, TMTT Jan. 2012 8-20 Electric admittance measurement Simulation and Measurement of the -Parameters of Obstacles in Periodic Waveguides. Navarro-Tapia, M., +, TMTT April 2012 1146-1155 Electric connectors Variability Analysis of Multiport Systems Via Polynomial-Chaos Expansion. Spina, D., +, TMTT Aug. 2012 2329-2338 Electric current measurement Controlling Active Load–Pull in a Dual-Input Inverse Load Modulated Doherty Architecture. Hone, T. M., +, TMTT June 2012 1797-1804 Electric impedance Design Method for Ultra-Wideband Bandpass Filter With Wide Stopband Using Parallel-Coupled Microstrip Lines. Abbosh, A. M., +, TMTT Jan. 2012 31-38 Fast Multiharmonic Active Load–Pull System With Waveform Measurement Capabilities. Thorsell, M., +, TMTT Jan. 2012 149-157 Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 Electric reactance Extremely Miniaturized Bandpass Filters Based on Asymmetric Coupled Lines With Equal Reactance. Park, J.-H., +, TMTT Feb. 2012 261-269 Electric resistance Comments on “Theoretical and Experimental Study of a New Class of Reflectionless Filter”. Roy, S. C. D., +, TMTT March 2012 632-633 Electric resistance measurement Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates. Evseev, S. B., +, TMTT Nov. 2012 3542-3550 Electro-optical modulation Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Electroforming Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses. Arnedo, I., +, TMTT May 2012 1244-1257 Electromagnetic compatibility Reproduction of the Effects of an Arbitrary Radiated Field by Ground Current Injection. Crovetti, P. S., +, TMTT April 2012 1136-1145 Electromagnetic coupling Crosstalk Reduction for Superconducting Microwave Resonator Arrays. Noroozian, O., +, TMTT May 2012 1235-1243 Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide. Zhang, L., +, TMTT Jan. 2012 1-7 Electromagnetic field theory Independence of the Unloaded of a Planar Electromagnetic Resonator From Its Shape. Naji, A., +, TMTT Aug. 2012 2370-2377

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TLM Extension to Electromagnetic Field Analysis of Anisotropic and Dispersive Media: A Unified Field Equation. Farhat, A. L., +, TMTT Aug. 2012 2339-2351 Electromagnetic fields Reproduction of the Effects of an Arbitrary Radiated Field by Ground Current Injection. Crovetti, P. S., +, TMTT April 2012 1136-1145 Electromagnetic interference Reproduction of the Effects of an Arbitrary Radiated Field by Ground Current Injection. Crovetti, P. S., +, TMTT April 2012 1136-1145 Electromagnetic wave absorption Development of Optically Transparent Ultrathin Microwave Absorber for Ultrahigh-Frequency RF Identification System. Okano, Y., +, TMTT Aug. 2012 2456-2464 Electromagnetic wave diffraction Diffraction in mm and Sub-mm Wave Indoor Propagation Channels. Jacob, M., +, TMTT March 2012 833-844 Electromagnetic wave polarization Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies. Bayatpur, F., +, TMTT April 2012 1126-1135 Electromagnetic wave propagation A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Broadband Electromagnetic Modeling of Woven Fabric Composites. Mirotznik, M. S., +, TMTT Jan. 2012 158-169 Finite-Element Eigenvalue Analysis of Propagating and Evanescent Modes in 3-D Periodic Structures Using Model-Order Reduction. Bostani, A., +, TMTT Sept. 2012 2677-2683 Electromagnetic wave reflection Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT March 2012 405-418 Electromagnetic wave scattering A Generalized Multiple Scattering Method for Dense Vias With Axially Anisotropic Modes in an Arbitrarily Shaped Plate Pair. Zhang, Y.-J., +, TMTT July 2012 2035-2045 Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies. Bayatpur, F., +, TMTT April 2012 1126-1135 Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems. Thomas, S. J., +, TMTT April 2012 1175-1182 Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation. Kilic, E., +, TMTT May 2012 14371443 Rigorous Derivation and Fast Solution of Spatial-Domain Green’s Functions for Uniaxial Anisotropic Multilayers Using Modified Fast Hankel Transform Method. Ding, P.-P., +, TMTT Feb. 2012 205-217 Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses. Arnedo, I., +, TMTT May 2012 1244-1257 Electromagnetic wave transmission Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT March 2012 405-418 Electromagnetic waveguides Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides. Ochoa, J. S., +, TMTT Dec. 2012 3919-3926 Inline Pseudoelliptic -Mode Dielectric Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Orthogonal Resonators. Bastioli, S., +, TMTT Dec. 2012 3988-4001 Electromagnetic waves A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters. Ahmed, O. S., +, TMTT Oct. 2012 2959-2971 Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Theory of Magnetic Transmission Lines. Brandao Faria, J. A., +, TMTT Oct. 2012 2941-2949 Electromagnetics Multiphysics Modeling of RF and Microwave High-Power Transistors. Aaen, P. H., +, TMTT Dec. 2012 4013-4023 Electron devices Guest Editorial. Popovic, Z., +, TMTT June 2012 1753-1754 Electronic engineering computing Parallel Frequency-Domain Simulation of Hyperspectral Waveforms in Nonlinear Power Amplifiers With Memory. Stantchev, G., +, TMTT April 2012 930-937

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Electronic equipment testing Reproduction of the Effects of an Arbitrary Radiated Field by Ground Current Injection. Crovetti, P. S., +, TMTT April 2012 1136-1145 Electronics packaging A Compact 3-D Harmonic Repeater for Passive Wireless Sensing. Nassar, I. T., +, TMTT Oct. 2012 3309-3316 Electrostatic actuators An All-Metal Micro-Relay With Bulk Foil Pt–Rh Contacts for High-Power RF Applications. Ozkeskin, F. M., +, TMTT June 2012 1595-1604 Electrostatic discharge 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process. Lin, C.-Y., +, TMTT March 2012 714-723 Elemental semiconductors A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process. Lin, C.-Y., +, TMTT March 2012 714-723 Miniaturized UWB Filters Integrated With Tunable Notch Filters Using a Silicon-Based Integrated Passive Device Technology. Wu, Z., +, TMTT March 2012 518-527 Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates. Evseev, S. B., +, TMTT Nov. 2012 3542-3550 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Elementary particle theory Polarization-Independent Metamaterial Analog of Electromagnetically Induced Transparency for a Refractive-Index-Based Sensor. Meng, F.-Y., +, TMTT Oct. 2012 3013-3022 Elliptic curves A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide. Lee, J.-W., +, TMTT Dec. 2012 3642-3655 Elliptic filters A Quasi Elliptic Function 1.75–2.25 GHz 3-Pole Bandpass Filter With Bandwidth Control. Chiou, Y.-C., +, TMTT Feb. 2012 244-249 Embedded systems A Digital-Intensive Multimode Multiband Receiver Using a Sinc FilterEmbedded VCO-Based ADC. Kim, J., +, TMTT Oct. 2012 3254-3262 Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 Equalizers Approach to the Design of Asymmetric Coupled-Line Directional Couplers With the Maximum Achievable Impedance-Transformation Ratio. Wincza, K., +, TMTT May 2012 1218-1225 Switchless Tunable Bandstop-to-All-Pass Reconfigurable Filter. Naglich, E. J., +, TMTT May 2012 1258-1265 Equivalent circuits A Broadband and Vialess Vertical Microstrip-to-Microstrip Transition. Huang, X., +, TMTT April 2012 938-944 A Broadband U-Slot Coupled Microstrip-to-Waveguide Transition. Huang, X., +, TMTT May 2012 1210-1217 A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 A Systematic Design Procedure of Classical Dual-Mode Circular Waveguide Filters Using an Equivalent Distributed Model. Cogollos, S., +, TMTT April 2012 1006-1017 An Equivalent Circuit for Discontinuities Exciting Evanescent Accessible Modes. Zappelli, L., +, TMTT May 2012 1197-1209 Design and Diagnosis of Wideband Coupled-Resonator Bandpass Filters. Lee, H.-M., +, TMTT May 2012 1266-1277 Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators. Ahn, H.-R., +, TMTT June 2012 1549-1559 Design of High-Order Wideband Planar Balun Filter in -Plane Bandpass Prototype. Lin, Y.-W., +, TMTT July 2012 2124-2130 Dual Composite Right-/Left-Handed Coplanar Waveguide Transmission Line Using Inductively Connected Split-Ring Resonators. Belenguer, A., +, TMTT Oct. 2012 3035-3042 + Check author entry for coauthors

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Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM. Zong, Z.-Y., +, TMTT June 2012 1500-1512 Hybrid Field/Transmission-Line Model for the Study of Coaxial Corrugated Waveguides. Savaidis, S. P., +, TMTT Oct. 2012 2972-2978 Interpolation-Based Parameterized Model Order Reduction of Delayed Systems. Ferranti, F., +, TMTT March 2012 431-440 in the Modeling Inductive Behavior of MOSFET Scattering Parameter Breakdown Regime. Lee, C.-I., +, TMTT March 2012 502-508 ParAFEMCap: A Parallel Adaptive Finite-Element Method for 3-D VLSI Interconnect Capacitance Extraction. Chen, G., +, TMTT Feb. 2012 218-231 Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT March 2012 405-418 Error statistics A 0.01–8-GHz (12.5 Gb/s) 4 4 CMOS Switch Matrix. Shin, D., +, TMTT Feb. 2012 381-386 Design and Analysis of a Low-Power 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance. Uzunkol, M., +, TMTT Oct. 2012 32633271 Etching Common-Mode Suppression in Microstrip Differential Lines by Means of Complementary Split Ring Resonators: Theory and Applications. Naqui, J., +, TMTT Oct. 2012 3023-3034 F Fabrics Broadband Electromagnetic Modeling of Woven Fabric Composites. Mirotznik, M. S., +, TMTT Jan. 2012 158-169 Fast Fourier transforms Efficient Analysis of Substrate Integrated Waveguide Devices Using Hybrid Mode Matching Between Cylindrical and Guided Modes. Diaz Caballero, E., +, TMTT Feb. 2012 232-243 Feature extraction Buried Object Characterization Using Ultra-Wideband Ground Penetrating Radar. Li, L., +, TMTT Aug. 2012 2654-2664 Feedback 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Modified Least Squares Extraction for Volterra-Series Digital Predistorter in the Presence of Feedback Measurement Errors. Liu, Y.-J., +, TMTT Nov. 2012 3559-3570 Feedback oscillators Design of a Direct Conversion Transmitter to Resist Combined Effects of Power Amplifier Distortion and Local Oscillator Pulling. Hsiao, C.-H., +, TMTT June 2012 2000-2009 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Feedforward amplifiers 0.6–3-GHz Wideband Receiver RF Front-End With a Feedforward Noise and Distortion Cancellation Resistive-Feedback LNA. Wang, X., +, TMTT Feb. 2012 387-392 Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078 Ferromagnetic materials A Comprehensive Analysis of the Absorption Spectrum of Conducting Ferromagnetic Wires. Liberal, I., +, TMTT July 2012 2055-2065 Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 Self-Biased Nonreciprocal Microstrip Phase Shifter on Magnetic Nanowired Substrate Suitable for Gyrator Applications. Hamoir, G., +, TMTT July 2012 2152-2157 Ferromagnetic resonance Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 FETs Resistive Graphene FET Subharmonic Mixers: Noise and Linearity Assessment. Andersson, M. A., +, TMTT Dec. 2012 4035-4042

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Field effect MIMIC -Band and -Band Power Amplifiers in 45-nm CMOS SOI. Kim, J., +, TMTT June 2012 1870-1877 60-GHz Dual-Conversion Down-/Up-Converters Using Schottky Diode in 0.18 m Foundry CMOS Technology. Wei, H.-J., +, TMTT June 2012 16841698 A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array. Kim, C.-Y., +, TMTT March 2012 730-742 A Full 360 Vector-Sum Phase Shifter With Very Low RMS Phase Error Over a Wide Bandwidth. Asoodeh, A., +, TMTT June 2012 1626-1634 A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 An Improved Wideband All-Pass I/Q Network for Millimeter-Wave Phase Shifters. Kim, S. Y., +, TMTT Nov. 2012 3431-3439 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Design and Analysis of a -band Divide-by-Three Injection-Locked Frequency Divider Using Second Harmonic Enhancement Technique. Yeh, Y.-L., +, TMTT June 2012 1617-1625 Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation. Jooyaie, A., +, TMTT Aug. 2012 2505-2511 Parasitic-Insensitive Linearization Methods for 60-GHz 90-nm CMOS LNAs. Li, W.-T., +, TMTT Aug. 2012 2512-2523 Field effect MMIC A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator. Lee, S., +, TMTT May 2012 1405-1412 A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 A Dual-Band 10/24-GHz Amplifier Design Incorporating Dual-Frequency Complex Load Matching. Hsieh, K.-A., +, TMTT June 2012 1649-1657 A Highly Reconfigurable Low-Power CMOS Directional Coupler. Sun, J., +, TMTT Sept. 2012 2815-2822 A Low-Voltage, Low-Power, and Low-Noise UWB Mixer Using Bulk-Injection and Switched Biasing Techniques. Kim, M.-G., +, TMTT Aug. 2012 2486-2493 A Narrowband CMOS Ring Resonator Dual-Mode Active Bandpass Filter With Edge Periphery of 2% Free-Space Wavelength. Su, L., +, TMTT June 2012 1605-1616 Low-Voltage -Band Divide-by-3 Injection-Locked Frequency Divider With Floating-Source Differential Injector. Chen, Y.-T., +, TMTT Jan. 2012 60-67 Theoretical Analysis and Practical Considerations for the Integrated TimeStretching System Using Dispersive Delay Line (DDL). Xiang, B., +, TMTT Nov. 2012 3449-3457 Field effect transistor switches Conformal Ink-Jet Printed -Band Phased-Array Antenna Incorporating Carbon Nanotube Field-Effect Transistor Based Reconfigurable True-Time Delay Lines. Chen, M. Y., +, TMTT Jan. 2012 179-184 Field effect transistors Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 Field programmable gate arrays Closed-Loop Digital Predistortion System With Fast Real-Time Adaptation Applied to a Handset WCDMA PA Module. Presti, C. D., +, TMTT March 2012 604-618 Filtering theory A -Band Fully Tunable Cavity Filter. Yassini, B., +, TMTT Dec. 2012 4002-4012 A Digital-Intensive Multimode Multiband Receiver Using a Sinc FilterEmbedded VCO-Based ADC. Kim, J., +, TMTT Oct. 2012 3254-3262 Inline Pseudoelliptic -Mode Dielectric Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Orthogonal Resonators. Bastioli, S., +, TMTT Dec. 2012 3988-4001 Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines. Sun, J. S., +, TMTT Dec. 2012 3950-3958 Narrowband Microwave Filters With Mixed Topology. Macchiarella, G., +, TMTT Dec. 2012 3980-3987 Wideband Dual-Mode Microstrip Filter Using Short-Ended Resonator With Centrally Loaded Inductive Stub. Sun, S.-J., +, TMTT Dec. 2012 3667-3673

+ Check author entry for coauthors

Filters An Ultra-Compact, Linearly-Controlled Variable Phase Shifter Designed With a Novel RC Poly-Phase Filter. Huang, Y.-Y., +, TMTT Feb. 2012 301-310 Application of Stepped-Impedance Technique for Bandwidth Control of Dual-Band Filters. Ha, J., +, TMTT July 2012 2106-2114 Synthesis of Vertical Interdigital Filters Using Multilayered Technologies. Perigaud, A., +, TMTT April 2012 965-974 Finite difference methods A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Ear Temperature Increase Produced by Cellular Phones Under Extreme Exposure Conditions. De Santis, V., +, TMTT June 2012 1728-1734 FDTD Modeling of Impedance Boundary Conditions by Equivalent LTI Circuits. Feliziani, M., +, TMTT Dec. 2012 3656-3666 Finite difference time domain analysis Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures. Dadash, M. S., +, TMTT Sept. 2012 2713-2722 In Vitro Dosimetry and Temperature Evaluations of a Typical MillimeterWave Aperture-Field Exposure Setup. Zhao, J., +, TMTT Nov. 2012 36083622 Finite element analysis A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the Turnstile Waveguide Circulator. Helszajn, J., +, TMTT Oct. 2012 3079-3087 Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures. Dadash, M. S., +, TMTT Sept. 2012 2713-2722 Authors’ reply. Chen, G., +, TMTT June 2012 1745-1747 Finite-Element Eigenvalue Analysis of Propagating and Evanescent Modes in 3-D Periodic Structures Using Model-Order Reduction. Bostani, A., +, TMTT Sept. 2012 2677-2683 Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements. Hu, F.-G., +, TMTT July 2012 2046-2054 ParAFEMCap: A Parallel Adaptive Finite-Element Method for 3-D VLSI Interconnect Capacitance Extraction. Chen, G., +, TMTT Feb. 2012 218-231 SPICE Lumped Circuit Subcell Model for the Discontinuous Galerkin Finite-Element Time-Domain Method. Zhao, B., +, TMTT Sept. 2012 26842692 Theoretical Design and Analysis for – Rectangular Waveguide Mode Converters. Zhang, Q., +, TMTT April 2012 1018-1026 Flip-chip devices 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 A Fully SiP Integrated -Band Butler Matrix End-Fire Beam-Switching Transmitter Using Flip-Chip Assembled CMOS Chips on LTCC. Kuo, C.-C., +, TMTT May 2012 1424-1436 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 Vertical RF Transition With Mechanical Fit for 3-D Heterogeneous Integration. Chen, L., +, TMTT March 2012 647-654 FM radar A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar. Jahn, M., +, TMTT March 2012 861-869 A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading. Koswatta, R. V., +, TMTT Sept. 2012 2925-2933 An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer. Pohl, N., +, TMTT March 2012 757-765 Focusing Terahertz Aperture Synthesized Imaging With Fan-Beam Scanning for Personnel Screening. Gu, S., +, TMTT Dec. 2012 3877-3885 Fourier analysis Formulation for Complete and Accurate Calibration of Six-Port Reflectometer. Haddadi, K., +, TMTT March 2012 574-581 Fourier transform spectra Microwave Chemical Sensing at Room Temperature Using an Overmoded Waveguide Design. Huang, Y.-T., +, TMTT Sept. 2012 2886-2893

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Fourier transforms Theoretical Analysis and Practical Considerations for the Integrated TimeStretching System Using Dispersive Delay Line (DDL). Xiang, B., +, TMTT Nov. 2012 3449-3457 Frequency control A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 Frequency conversion A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer. Tang, A., +, TMTT Dec. 2012 4129-4137 A 64–84-GHz PLL With Low Phase Noise in an 80-GHz SiGe HBT Technology. Liu, G., +, TMTT Dec. 2012 3739-3748 Coupled Line 180 Hybrids With Lange Couplers. Napijalo, V., +, TMTT Dec. 2012 3674-3682 Design and Analysis of Digital-Assisted Bandwidth-Enhanced Miller Divider in 0.18- m CMOS Process. Kuo, Y.-H., +, TMTT Dec. 2012 37693777 PA Efficiency and Linearity Enhancement Using External Harmonic Injection. Dani, A., +, TMTT Dec. 2012 4097-4106 Passive Subharmonic Generation Using Memoryless Nonlinear Circuits. Safarian, Z., +, TMTT Dec. 2012 4053-4065 Frequency dividers -band Divide-by-Three Injection-Locked Design and Analysis of a Frequency Divider Using Second Harmonic Enhancement Technique. Yeh, Y.-L., +, TMTT June 2012 1617-1625 Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Low-Voltage -Band Divide-by-3 Injection-Locked Frequency Divider With Floating-Source Differential Injector. Chen, Y.-T., +, TMTT Jan. 2012 60-67 Low-Voltage, Wide-Locking-Range, Millimeter-Wave Divide-by-5 Injection-Locked Frequency Dividers. Li, M.-W., +, TMTT March 2012 679-685 Frequency domain analysis Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers. Yu, C., +, TMTT Dec. 2012 4198-4208 Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach. Kabir, M., +, TMTT Dec. 2012 3927-3938 Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes. Suarez, A., +, TMTT March 2012 528-541 Theory of Magnetic Transmission Lines. Brandao Faria, J. A., +, TMTT Oct. 2012 2941-2949 Frequency estimation Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines. Sun, J. S., +, TMTT Dec. 2012 3950-3958 Frequency measurement Resistive Graphene FET Subharmonic Mixers: Noise and Linearity Assessment. Andersson, M. A., +, TMTT Dec. 2012 4035-4042 Frequency modulation A Modified Doherty Configuration for Broadband Amplification Using Symmetrical Devices. Wu, D. Y.-T., +, TMTT Oct. 2012 3201-3213 Frequency multipliers -Band Amplifiers With 6-dB Noise Figure and Milliwatt-Level 170–200-GHz Doublers in 45-nm CMOS. Cetinoneri, B., +, TMTT March 2012 692-701 A Waveform-Dependent Phase-Noise Analysis for Edge-Combining DLL Frequency Multipliers. Liao, F.-R., +, TMTT April 2012 1086-1096 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 W-Band Silicon-Based Frequency Synthesizers Using Injection-Locked and Harmonic Triplers. Wang, C.-C., +, TMTT May 2012 1307-1320 Frequency response An Instrumental Variable Vector-Fitting Approach for Noisy Frequency Responses. Beygi, A., +, TMTT Sept. 2012 2702-2712 Autoregressive Modeling of Mobile Radio Propagation Channel in Building Ruins. Chen, L., +, TMTT May 2012 1478-1489 Experimental Characterization of Stability Margins in Microwave Amplifiers. Otegi, N., +, TMTT Dec. 2012 4145-4156

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Millimeter-Wave Optoelectronic Mixers Based on Uni-Traveling Carrier Photodiodes. Rouvalis, E., +, TMTT March 2012 686-691 Mitigation of Bandwidth Limitation in Wireless Doherty Amplifiers With Substantial Bandwidth Enhancement Using Digital Techniques. Darraji, R., +, TMTT Sept. 2012 2875-2885 Frequency selective surfaces A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 Frequency shift keying A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 Frequency stability Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Frequency synchronization Passive Subharmonic Generation Using Memoryless Nonlinear Circuits. Safarian, Z., +, TMTT Dec. 2012 4053-4065 Frequency synthesizers A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer. Tang, A., +, TMTT Dec. 2012 4129-4137 A Self-Sustained Microwave System for Dielectric-Constant Measurement of Lossy Organic Liquids. Sekar, V., +, TMTT May 2012 1444-1455 Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Functions Exact and Closed-Form Cutoff Wavenumbers of Elliptical Dielectric Waveguides. Zouros, G. P., +, TMTT Sept. 2012 2741-2751

G Gain 4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers. Aja Abelan, B., +, TMTT Dec. 2012 4080-4088 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications. Son, K. Y., +, TMTT Aug. 2012 2571-2580 A Fully Integrated Adaptive Multiband Multimode Switching-Mode CMOS Power Amplifier. Aref, A. F., +, TMTT Aug. 2012 2549-2561 Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique. Yeh, H.-C., +, TMTT Dec. 2012 4066-4079 Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin. Ziegler, V., +, TMTT Dec. 2012 4209-4219 Galerkin method A New High-Efficient Spectral-Domain Analysis of Single and Multiple Coupled Microstrip Lines in Planarly Layered Media. Lucido, M., +, TMTT July 2012 2025-2034 A Spurious-Free Discontinuous Galerkin Time-Domain Method for the Accurate Modeling of Microwave Filters. Alvarez, J., +, TMTT Aug. 2012 2359-2369 Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements. Hu, F.-G., +, TMTT July 2012 2046-2054 SPICE Lumped Circuit Subcell Model for the Discontinuous Galerkin Finite-Element Time-Domain Method. Zhao, B., +, TMTT Sept. 2012 26842692 Gallium arsenide 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules. Florian, C., +, TMTT June 2012 1805-1816 A 17–35 GHz Broadband, High Efficiency PHEMT Power Amplifier Using Synthesized Transformer Matching Technique. Huang, P.-C., +, TMTT Jan. 2012 112-119 A 3-D Table-Based Method for Non-Quasi-Static Microwave FET Devices Modeling. Long, Y., +, TMTT Oct. 2012 3088-3095 A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607

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A Broadband Injection-Locking Class-E Power Amplifier. Lin, C.-H., +, TMTT Oct. 2012 3232-3242 A Novel Model for Implementation of Gamma Radiation Effects in GaAs HBTs. Zhang, J., +, TMTT Dec. 2012 3693-3698 A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications. Hassan, M., +, TMTT May 2012 1321-1330 Gain-Bandwidth Analysis of Broadband Darlington Amplifiers in HBT-HEMT Process. Weng, S.-H., +, TMTT Nov. 2012 3458-3473 Generalization and Reduction of Line-Series-Shunt Calibration for Broadband GaAs and CMOS On-Wafer Scattering Parameter Measurements. Huang, C.-C., +, TMTT Dec. 2012 4138-4144 High-Efficiency Cellular Power Amplifiers Based on a Modified LDMOS Process on Bulk Silicon and Silicon-On-Insulator Substrates With Integrated Power Management Circuitry. Tombak, A., +, TMTT June 2012 1862-1869 Optimized Load Modulation Network for Doherty Power Amplifier Performance Enhancement. Chen, S., +, TMTT Nov. 2012 3474-3481 The Continuous Inverse Class-F Mode With Resistive Second-Harmonic Impedance. Carrubba, V., +, TMTT June 2012 1928-1936 Gallium compounds 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules. Florian, C., +, TMTT June 2012 1805-1816 3–3.6-GHz Wideband GaN Doherty Power Amplifier Exploiting Output Compensation Stages. Rubio, J. M., +, TMTT Aug. 2012 2543-2548 A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 A Simplified Broadband Design Methodology for Linearized High-Efficiency Continuous Class-F Power Amplifiers. Tuffy, N., +, TMTT June 2012 1952-1963 AlGaN/GaN HEMT With Distributed Gate for Channel Temperature Reduction. Darwish, A. M., +, TMTT April 2012 1038-1043 Analysis and Implementation of Doherty Power Amplifier With Two-Point Envelope Modulation. Kim, J. H., +, TMTT May 2012 1353-1364 Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier. Saad, P., +, TMTT June 2012 1840-1849 Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828 Switching Behavior of Class-E Power Amplifier and Its Operation Above Maximum Frequency. Jee, S., +, TMTT Jan. 2012 89-98 Gallium nitride GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion. Garcia, J. A., +, TMTT Dec. 2012 4220-4229 Gaussian processes Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks. Cantu, H. I., +, TMTT Sept. 2012 2903-2912 Ge-Si alloys -Band Total Power Radiometer Performance Optimization in an SiGe HBT Technology. Dacquay, E., +, TMTT March 2012 813-826 A 1.1-V Regulator-Stabilized 21.4-GHz VCO and a 115% Frequency-Range Dynamic Divider for -Band Wireless Communication. Nakamura, T., +, TMTT Sept. 2012 2823-2832 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array. Kim, C.-Y., +, TMTT March 2012 730-742 Modulator for Switch-Mode Power A 5-Gb/s 2.1–2.2-GHz Bandpass Amplifier. Ostrovskyy, P., +, TMTT Aug. 2012 2524-2531 A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490

+ Check author entry for coauthors

A Compact Linear 60-GHz PA With 29.2% PAE Operating at Weak Avalanche Area in SiGe. Sun, Y., +, TMTT Aug. 2012 2581-2589 A Nested-Reactance Feedback Power Amplifier for -Band Applications. Kalantari, N., +, TMTT June 2012 1667-1675 A Transformer-Coupling Current-Reuse SiGe HBT Power Amplifier for 77-GHz Automotive Radar. Giammello, V., +, TMTT June 2012 1676-1683 An Improved Wideband All-Pass I/Q Network for Millimeter-Wave Phase Shifters. Kim, S. Y., +, TMTT Nov. 2012 3431-3439 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Analysis and Design of a Stacked Power Amplifier With Very High Bandwidth. Fritsche, D., +, TMTT Oct. 2012 3223-3231 Design and Analysis of a Low-Power 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance. Uzunkol, M., +, TMTT Oct. 2012 32633271 Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators. Gupta, A. K., +, TMTT Oct. 2012 3272-3285 Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 Systematic Compact Modeling of Correlated Noise in Bipolar Transistors. Herricht, J., +, TMTT Nov. 2012 3403-3412 Ultrafast Low-Loss 42–70 GHz Differential SPDT Switch in 0.35 m SiGe Technology. Thian, M., +, TMTT March 2012 655-659 Geometrical optics Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM. Zong, Z.-Y., +, TMTT June 2012 1500-1512 Geometry On the Relation Between Stored Energy and Fabrication Tolerances in Microwave Filters. Martinez-Mendoza, M., +, TMTT July 2012 2131-2141 Germanium compounds A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar. Jahn, M., +, TMTT March 2012 861-869 An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer. Pohl, N., +, TMTT March 2012 757-765 Ginzburg-Landau theory A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Global Positioning System Reconfigurable Dual-Channel Multiband RF Receiver for GPS/ Galileo/BD-2 Systems. Chen, D., +, TMTT Nov. 2012 3491-3501 Graphene Gyrotropy and Nonreciprocity of Graphene for Microwave Applications. Sounas, D. L., +, TMTT April 2012 901-914 Graphics processing units MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit. De Donno, D., +, TMTT Sept. 2012 2693-2701 Gratings Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT Dec. 2012 3908-3918 Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings. Memarian, M., +, TMTT Dec. 2012 3893-3907 Green’s function methods Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM. Zong, Z.-Y., +, TMTT June 2012 1500-1512 Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings. Memarian, M., +, TMTT Dec. 2012 3893-3907 Rigorous Derivation and Fast Solution of Spatial-Domain Green’s Functions for Uniaxial Anisotropic Multilayers Using Modified Fast Hankel Transform Method. Ding, P.-P., +, TMTT Feb. 2012 205-217 Ground penetrating radar Buried Object Characterization Using Ultra-Wideband Ground Penetrating Radar. Li, L., +, TMTT Aug. 2012 2654-2664 Gyrators Self-Biased Nonreciprocal Microstrip Phase Shifter on Magnetic Nanowired Substrate Suitable for Gyrator Applications. Hamoir, G., +, TMTT July 2012 2152-2157 Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

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Hankel transforms Efficient Analysis of Substrate Integrated Waveguide Devices Using Hybrid Mode Matching Between Cylindrical and Guided Modes. Diaz Caballero, E., +, TMTT Feb. 2012 232-243 Rigorous Derivation and Fast Solution of Spatial-Domain Green’s Functions for Uniaxial Anisotropic Multilayers Using Modified Fast Hankel Transform Method. Ding, P.-P., +, TMTT Feb. 2012 205-217 Harmonic analysis A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer. Tang, A., +, TMTT Dec. 2012 4129-4137 Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT Dec. 2012 3908-3918 Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier Using In-Band Continuous Class-F F Mode Transferring. Chen, K., +, TMTT Dec. 2012 4107-4116 High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers. Roberg, M., +, TMTT Dec. 2012 4043-4052 PA Efficiency and Linearity Enhancement Using External Harmonic Injection. Dani, A., +, TMTT Dec. 2012 4097-4106 Theory and Design of Class-J Power Amplifiers With Dynamic Load Modulation. Andersson, C. M., +, TMTT Dec. 2012 3778-3786 Harmonic distortion Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links. Alcaro, G., +, TMTT Jan. 2012 185-194 Large-Signal Oscillator Design Procedure Utilizing Analytical -Parameters Closed-Form Expressions. Pelaez-Perez, A. M., +, TMTT Oct. 2012 3126-3136 Harmonic generation An Analytical Formulation for Black Box Conversion Matrix Extraction. Kheirdoost, A., +, TMTT June 2012 1493-1499 Harmonics 3–3.6-GHz Wideband GaN Doherty Power Amplifier Exploiting Output Compensation Stages. Rubio, J. M., +, TMTT Aug. 2012 2543-2548 Harmonics suppression Harmonic Suppressed Dual-Band Bandpass Filters With Tunable Passbands. Chaudhary, G., +, TMTT July 2012 2115-2123 Novel Wideband Differential Bandpass Filters Based on T-Shaped Structure. Feng, W., +, TMTT June 2012 1560-1568 Phase Velocities Equalization of Coupled Microstrip Lines Using -Shaped Particles and Suppression of the Second Harmonic. Hatefi Ardakani, H., +, TMTT March 2012 464-470 Stepped-Impedance Coupled Resonators for Implementation of Parallel Coupled Microstrip Filters With Spurious Band Suppression. Worapishet, A., +, TMTT June 2012 1540-1548 Heating Ear Temperature Increase Produced by Cellular Phones Under Extreme Exposure Conditions. De Santis, V., +, TMTT June 2012 1728-1734 Helical waveguides Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide. Zhang, L., +, TMTT Jan. 2012 1-7 HEMT integrated circuits 3–3.6-GHz Wideband GaN Doherty Power Amplifier Exploiting Output Compensation Stages. Rubio, J. M., +, TMTT Aug. 2012 2543-2548 A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier. Saad, P., +, TMTT June 2012 1840-1849 GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion. Garcia, J. A., +, TMTT Dec. 2012 4220-4229 Novel MMIC Power Amplifier Linearization Utilizing Input Reflected Nonlinearity. Kuo, N.-C., +, TMTT March 2012 542-554 Power Amplification at 0.65 THz Using InP HEMTs. Radisic, V., +, TMTT March 2012 724-729 Heterojunction bipolar transistors -Band Total Power Radiometer Performance Optimization in an SiGe HBT Technology. Dacquay, E., +, TMTT March 2012 813-826 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules. Florian, C., +, TMTT June 2012 1805-1816 + Check author entry for coauthors

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A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A Compact Linear 60-GHz PA With 29.2% PAE Operating at Weak Avalanche Area in SiGe. Sun, Y., +, TMTT Aug. 2012 2581-2589 A Novel Model for Implementation of Gamma Radiation Effects in GaAs HBTs. Zhang, J., +, TMTT Dec. 2012 3693-3698 A Transformer-Coupling Current-Reuse SiGe HBT Power Amplifier for 77-GHz Automotive Radar. Giammello, V., +, TMTT June 2012 1676-1683 A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications. Hassan, M., +, TMTT May 2012 1321-1330 Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range. Voinigescu, S. P., +, TMTT Dec. 2012 4024-4034 Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology. Kuylenstierna, D., +, TMTT Nov. 2012 3420-3430 Gain-Bandwidth Analysis of Broadband Darlington Amplifiers in HBT-HEMT Process. Weng, S.-H., +, TMTT Nov. 2012 3458-3473 Subharmonic 220- and 320-GHz SiGe HBT Receiver Front-Ends. Ojefors, E., +, TMTT May 2012 1397-1404 Systematic Compact Modeling of Correlated Noise in Bipolar Transistors. Herricht, J., +, TMTT Nov. 2012 3403-3412 HF amplifiers Modeling and Digital Predistortion of Class-D Outphasing RF Power Amplifiers. Landin, P. N., +, TMTT June 2012 1907-1915 High electron mobility transistors 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission. Hirata, A., +, TMTT March 2012 881-895 A 17–35 GHz Broadband, High Efficiency PHEMT Power Amplifier Using Synthesized Transformer Matching Technique. Huang, P.-C., +, TMTT Jan. 2012 112-119 A Broadband Injection-Locking Class-E Power Amplifier. Lin, C.-H., +, TMTT Oct. 2012 3232-3242 A Dual-Band Parallel Doherty Power Amplifier for Wireless Applications. Grebennikov, A., +, TMTT Oct. 2012 3214-3222 A High-Efficiency Low-Distortion GaN HEMT Doherty Power Amplifier With a Series-Connected Load. Kawai, S., +, TMTT Feb. 2012 352-360 A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 A Simplified Broadband Design Methodology for Linearized High-Efficiency Continuous Class-F Power Amplifiers. Tuffy, N., +, TMTT June 2012 1952-1963 AlGaN/GaN HEMT With Distributed Gate for Channel Temperature Reduction. Darwish, A. M., +, TMTT April 2012 1038-1043 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 Gain-Bandwidth Analysis of Broadband Darlington Amplifiers in HBT-HEMT Process. Weng, S.-H., +, TMTT Nov. 2012 3458-3473 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 Optimized Load Modulation Network for Doherty Power Amplifier Performance Enhancement. Chen, S., +, TMTT Nov. 2012 3474-3481 Security Pre-screening of Moving Persons Using a Rotating Multichannel -Band Radar. Hantscher, S., +, TMTT March 2012 870-880 Switching Behavior of Class-E Power Amplifier and Its Operation Above Maximum Frequency. Jee, S., +, TMTT Jan. 2012 89-98 The Continuous Inverse Class-F Mode With Resistive Second-Harmonic Impedance. Carrubba, V., +, TMTT June 2012 1928-1936 Vectorially Combined Distributed Power Amplifiers for Software-Defined Radio Applications. Narendra, K., +, TMTT Oct. 2012 3189-3200 High-frequency effects Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 High-frequency transformers Analysis and Design of a 60 GHz Wideband Voltage-Voltage Transformer Feedback LNA. Sakian, P., +, TMTT March 2012 702-713 High-Performance Solenoidal RF Transformers on High-Resistivity Silicon Substrates for 3D Integrated Circuits. Feng, Z., +, TMTT July 2012 20662072 High-frequency transmission lines Optimized Load Modulation Network for Doherty Power Amplifier Performance Enhancement. Chen, S., +, TMTT Nov. 2012 3474-3481

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High-speed integrated circuits Interpolation-Based Parameterized Model Order Reduction of Delayed Systems. Ferranti, F., +, TMTT March 2012 431-440 Hilbert transforms A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading. Koswatta, R. V., +, TMTT Sept. 2012 2925-2933 Hysteresis Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes. Suarez, A., +, TMTT March 2012 528-541

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III-V semiconductors 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules. Florian, C., +, TMTT June 2012 1805-1816 3–3.6-GHz Wideband GaN Doherty Power Amplifier Exploiting Output Compensation Stages. Rubio, J. M., +, TMTT Aug. 2012 2543-2548 A 17–35 GHz Broadband, High Efficiency PHEMT Power Amplifier Using Synthesized Transformer Matching Technique. Huang, P.-C., +, TMTT Jan. 2012 112-119 A 3-D Table-Based Method for Non-Quasi-Static Microwave FET Devices Modeling. Long, Y., +, TMTT Oct. 2012 3088-3095 A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 A Simplified Broadband Design Methodology for Linearized High-Efficiency Continuous Class-F Power Amplifiers. Tuffy, N., +, TMTT June 2012 1952-1963 A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications. Hassan, M., +, TMTT May 2012 1321-1330 AlGaN/GaN HEMT With Distributed Gate for Channel Temperature Reduction. Darwish, A. M., +, TMTT April 2012 1038-1043 Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters. Hoversten, J., +, TMTT June 2012 2010-2020 Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier. Saad, P., +, TMTT June 2012 1840-1849 Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology. Kuylenstierna, D., +, TMTT Nov. 2012 3420-3430 Gain-Bandwidth Analysis of Broadband Darlington Amplifiers in HBT-HEMT Process. Weng, S.-H., +, TMTT Nov. 2012 3458-3473 High-Efficiency Cellular Power Amplifiers Based on a Modified LDMOS Process on Bulk Silicon and Silicon-On-Insulator Substrates With Integrated Power Management Circuitry. Tombak, A., +, TMTT June 2012 1862-1869 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828 Optimized Load Modulation Network for Doherty Power Amplifier Performance Enhancement. Chen, S., +, TMTT Nov. 2012 3474-3481 Power Amplification at 0.65 THz Using InP HEMTs. Radisic, V., +, TMTT March 2012 724-729 Switching Behavior of Class-E Power Amplifier and Its Operation Above Maximum Frequency. Jee, S., +, TMTT Jan. 2012 89-98 The Continuous Inverse Class-F Mode With Resistive Second-Harmonic Impedance. Carrubba, V., +, TMTT June 2012 1928-1936 + Check author entry for coauthors

Image processing Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM. Zong, Z.-Y., +, TMTT June 2012 1500-1512 Image reconstruction Terahertz Aperture Synthesized Imaging With Fan-Beam Scanning for Personnel Screening. Gu, S., +, TMTT Dec. 2012 3877-3885 Image resolution Terahertz Aperture Synthesized Imaging With Fan-Beam Scanning for Personnel Screening. Gu, S., +, TMTT Dec. 2012 3877-3885 Immunity testing Reproduction of the Effects of an Arbitrary Radiated Field by Ground Current Injection. Crovetti, P. S., +, TMTT April 2012 1136-1145 Impact ionization in the Modeling Inductive Behavior of MOSFET Scattering Parameter Breakdown Regime. Lee, C.-I., +, TMTT March 2012 502-508 Impedance A Modified Doherty Configuration for Broadband Amplification Using Symmetrical Devices. Wu, D. Y.-T., +, TMTT Oct. 2012 3201-3213 A Physics-Based Causal Bond-Wire Model for RF Applications. Nazarian, A. L., +, TMTT Dec. 2012 3683-3692 A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN. Chen, J.-H., +, TMTT Dec. 2012 4089-4096 Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT Dec. 2012 3908-3918 CMOS Integrated Antenna-Coupled Field-Effect Transistors for the Detection of Radiation From 0.2 to 4.3 THz. Boppel, S., +, TMTT Dec. 2012 3834-3843 Design and Analysis of Digital-Assisted Bandwidth-Enhanced Miller Divider in 0.18- m CMOS Process. Kuo, Y.-H., +, TMTT Dec. 2012 37693777 Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier Using In-Band Continuous Class-F F Mode Transferring. Chen, K., +, TMTT Dec. 2012 4107-4116 FDTD Modeling of Impedance Boundary Conditions by Equivalent LTI Circuits. Feliziani, M., +, TMTT Dec. 2012 3656-3666 High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers. Roberg, M., +, TMTT Dec. 2012 4043-4052 On the Compression and Blocking Distortion of Semiconductor-Based Varactors. Huang, C., +, TMTT Dec. 2012 3699-3709 Theory and Design of Class-J Power Amplifiers With Dynamic Load Modulation. Andersson, C. M., +, TMTT Dec. 2012 3778-3786 Variable Reflection-Type Attenuators Based on Varactor Diodes. Bulja, S., +, TMTT Dec. 2012 3719-3727 Widely Tunable High-Efficiency Power Amplifier With Ultra-Narrow Instantaneous Bandwidth. Chen, K., +, TMTT Dec. 2012 3787-3797 Impedance converters A Fully Integrated Watt-Level Linear 900-MHz CMOS RF Power Amplifier for LTE-Applications. Francois, B., +, TMTT June 2012 1878-1885 A Novel Dual-Band 3-dB Branch-Line Coupler Design With Controllable Bandwidths. Cheng, K.-K. M., +, TMTT Oct. 2012 3055-3061 A Transformer-Less Load-Modulated (TLLM) Architecture for Efficient Wideband Power Amplifiers. Akbarpour, M., +, TMTT Sept. 2012 2863-2874 Approach to the Design of Asymmetric Coupled-Line Directional Couplers With the Maximum Achievable Impedance-Transformation Ratio. Wincza, K., +, TMTT May 2012 1218-1225 Cascaded Coupled Line Filter With Reconfigurable Bandwidths Using LCP Multilayer Circuit Technology. Miller, A., +, TMTT June 2012 1577-1586 Complex Impedance Transformers Consisting of Only Transmission-Line Sections. Ahn, H.-R., +, TMTT July 2012 2073-2084 Design of Compact Quad-Frequency Impedance Transformer Using TwoSection Coupled Line. Bai, Y.-F., +, TMTT Aug. 2012 2417-2423 Design of Multiway Power Divider by Using Stepped-Impedance Transformers. Xu, Y., +, TMTT Sept. 2012 2781-2790 Ultra-Wideband Single and Dual Baluns Based on Substrate Integrated Coaxial Line Technology. Zhu, F., +, TMTT Oct. 2012 3062-3070 Unequal Wilkinson Power Dividers With Favorable Selectivity and HighIsolation Using Coupled-Line Filter Transformers. Deng, P.-H., +, TMTT June 2012 1520-1529 Impedance matching Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter. Lin, F., +, TMTT May 2012 1226-1234

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Design of Compact Quad-Frequency Impedance Transformer Using TwoSection Coupled Line. Bai, Y.-F., +, TMTT Aug. 2012 2417-2423 Distributed Modeling of Six-Port Transformer for Millimeter-Wave SiGe BiCMOS Circuits Design. Hou, D., +, TMTT Dec. 2012 3728-3738 Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT March 2012 405-418 Impedance matrix MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit. De Donno, D., +, TMTT Sept. 2012 2693-2701 Indium compounds 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules. Florian, C., +, TMTT June 2012 1805-1816 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission. Hirata, A., +, TMTT March 2012 881-895 Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology. Kuylenstierna, D., +, TMTT Nov. 2012 3420-3430 Power Amplification at 0.65 THz Using InP HEMTs. Radisic, V., +, TMTT March 2012 724-729 Indium phosphide Guest Editorial. Rebeiz, G. M., +, TMTT March 2012 637-639 Inductance 245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology. Mao, Y., +, TMTT Dec. 2012 3823-3833 A Physics-Based Causal Bond-Wire Model for RF Applications. Nazarian, A. L., +, TMTT Dec. 2012 3683-3692 Inductance measurement Device Characterization Techniques Based on Causal Relationships. Wojnowski, M., +, TMTT July 2012 2203-2219 Inductive power transmission Low-Power Wireless Power Delivery. Falkenstein, E., +, TMTT July 2012 2277-2286 Inductors A Dual-Resonant Mode 10/22-GHz VCO With a Novel Inductive Switching Approach. Liu, S.-L., +, TMTT July 2012 2165-2177 A Highly Reconfigurable Low-Power CMOS Directional Coupler. Sun, J., +, TMTT Sept. 2012 2815-2822 A Nonlinear Lattice for High-Amplitude Picosecond Pulse Generation in CMOS. Lee, W., +, TMTT Feb. 2012 370-380 Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique. Yeh, H.-C., +, TMTT Dec. 2012 4066-4079 Crosstalk Reduction for Superconducting Microwave Resonator Arrays. Noroozian, O., +, TMTT May 2012 1235-1243 Design and Diagnosis of Wideband Coupled-Resonator Bandpass Filters. Lee, H.-M., +, TMTT May 2012 1266-1277 Distributed Modeling of Six-Port Transformer for Millimeter-Wave SiGe BiCMOS Circuits Design. Hou, D., +, TMTT Dec. 2012 3728-3738 Portable Space Mapping for Efficient Statistical Modeling of Passive Components. Zhang, L., +, TMTT March 2012 441-450 Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078 Inhomogeneous media A New High-Efficient Spectral-Domain Analysis of Single and Multiple Coupled Microstrip Lines in Planarly Layered Media. Lucido, M., +, TMTT July 2012 2025-2034 Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM. Zong, Z.-Y., +, TMTT June 2012 1500-1512 Injection locked amplifiers A Broadband Injection-Locking Class-E Power Amplifier. Lin, C.-H., +, TMTT Oct. 2012 3232-3242 Injection locked oscillators Experimental Characterization of Oscillator Circuits for Reduced-Order Models. Umpierrez, P., +, TMTT Nov. 2012 3527-3541 Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Low-Voltage, Wide-Locking-Range, Millimeter-Wave Divide-by-5 Injection-Locked Frequency Dividers. Li, M.-W., +, TMTT March 2012 679-685

+ Check author entry for coauthors

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Ink jet printing Conformal Ink-Jet Printed -Band Phased-Array Antenna Incorporating Carbon Nanotube Field-Effect Transistor Based Reconfigurable True-Time Delay Lines. Chen, M. Y., +, TMTT Jan. 2012 179-184 Insertion loss Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave. Wu, J., +, TMTT Dec. 2012 3959-3968 Variable Reflection-Type Attenuators Based on Varactor Diodes. Bulja, S., +, TMTT Dec. 2012 3719-3727 Instrumentation and measurement Guest Editorial. Popovic, Z., +, TMTT June 2012 1753-1754 Integral equations A New High-Efficient Spectral-Domain Analysis of Single and Multiple Coupled Microstrip Lines in Planarly Layered Media. Lucido, M., +, TMTT July 2012 2025-2034 A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide. Lee, J.-W., +, TMTT Dec. 2012 3642-3655 MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit. De Donno, D., +, TMTT Sept. 2012 2693-2701 Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation. Kilic, E., +, TMTT May 2012 14371443 Integrated circuit bonding 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 Integrated circuit design A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 An Open-Loop Half-Quadrature Hybrid for Multiphase Signals Generation. Chen, H.-S., +, TMTT Jan. 2012 131-138 Analysis and Design of 60-GHz SPDT Switch in 130-nm CMOS. He, J., +, TMTT Oct. 2012 3113-3119 Design of 40–108-GHz Low-Power and High-Speed CMOS Up-/DownConversion Ring Mixers for Multistandard MMW Radio Applications. Tsai, J.-H., +, TMTT March 2012 670-678 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 Interpolation-Based Parameterized Model Order Reduction of Delayed Systems. Ferranti, F., +, TMTT March 2012 431-440 Large-Signal Oscillator Design Procedure Utilizing Analytical -Parameters Closed-Form Expressions. Pelaez-Perez, A. M., +, TMTT Oct. 2012 3126-3136 Pulse-Biased Low-Power Low-Phase-Noise UHF LC-QVCO for 866 MHz RFID Front-End. Li, J., +, TMTT Oct. 2012 3120-3125 Simulation and Experiment of a Compact Wideband 90 Differential Phase Shifter. Sorn, M., +, TMTT March 2012 494-501 Subsampling Feedback Loop Applicable to Concurrent Dual-Band Linearization Architecture. Bassam, S. A., +, TMTT June 2012 1990-1999 Integrated circuit interconnections A Fully SiP Integrated -Band Butler Matrix End-Fire Beam-Switching Transmitter Using Flip-Chip Assembled CMOS Chips on LTCC. Kuo, C.-C., +, TMTT May 2012 1424-1436 An Instrumental Variable Vector-Fitting Approach for Noisy Frequency Responses. Beygi, A., +, TMTT Sept. 2012 2702-2712 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 ParAFEMCap: A Parallel Adaptive Finite-Element Method for 3-D VLSI Interconnect Capacitance Extraction. Chen, G., +, TMTT Feb. 2012 218-231 Variability Analysis of Multiport Systems Via Polynomial-Chaos Expansion. Spina, D., +, TMTT Aug. 2012 2329-2338 Vertical RF Transition With Mechanical Fit for 3-D Heterogeneous Integration. Chen, L., +, TMTT March 2012 647-654 Integrated circuit manufacture A High Dynamic-Range RF Programmable-Gain Front End for G.hn RF-Coax in 65-nm CMOS. Trulls, X., +, TMTT Oct. 2012 3243-3253 Novel MMIC Power Amplifier Linearization Utilizing Input Reflected Nonlinearity. Kuo, N.-C., +, TMTT March 2012 542-554

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Integrated circuit measurement Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 Integrated circuit modeling A Novel Model for Implementation of Gamma Radiation Effects in GaAs HBTs. Zhang, J., +, TMTT Dec. 2012 3693-3698 A Physics-Based Causal Bond-Wire Model for RF Applications. Nazarian, A. L., +, TMTT Dec. 2012 3683-3692 Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range. Voinigescu, S. P., +, TMTT Dec. 2012 4024-4034 Coupled Line 180 Hybrids With Lange Couplers. Napijalo, V., +, TMTT Dec. 2012 3674-3682 Distributed Modeling of Six-Port Transformer for Millimeter-Wave SiGe BiCMOS Circuits Design. Hou, D., +, TMTT Dec. 2012 3728-3738 FDTD Modeling of Impedance Boundary Conditions by Equivalent LTI Circuits. Feliziani, M., +, TMTT Dec. 2012 3656-3666 Multiphysics Modeling of RF and Microwave High-Power Transistors. Aaen, P. H., +, TMTT Dec. 2012 4013-4023 Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity. Ruiz-Cruz, J. A., +, TMTT Dec. 2012 3969-3979 Integrated circuit modelling Design of a Broadband Eight-Way Coaxial Waveguide Power Combiner. Amjadi, M., +, TMTT Jan. 2012 39-45 Interpolation-Based Parameterized Model Order Reduction of Delayed Systems. Ferranti, F., +, TMTT March 2012 431-440 Integrated circuit noise A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Integrated circuit packaging A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Vertical RF Transition With Mechanical Fit for 3-D Heterogeneous Integration. Chen, L., +, TMTT March 2012 647-654 Integrated circuit reliability Terahertz Micromachined On-Wafer Probes: Repeatability and Reliability. Chen, L., +, TMTT Sept. 2012 2894-2902 Integrated circuit testing Terahertz Micromachined On-Wafer Probes: Repeatability and Reliability. Chen, L., +, TMTT Sept. 2012 2894-2902 Integrated circuit yield Millimeter-Wave Self-Healing Power Amplifier With Adaptive Amplitude and Phase Linearization in 65-nm CMOS. Liu, J. Y.-C., +, TMTT May 2012 1342-1352 Integrated circuits Guest Editorial. Rieh, J.-S., +, TMTT Dec. 2012 3641 Integrated optoelectronics Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks. Cantu, H. I., +, TMTT Sept. 2012 2903-2912 Intensity modulation A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links. Alcaro, G., +, TMTT Jan. 2012 185-194 Interference (signal) A 130-nm CMOS 100-Hz–6-GHz Reconfigurable Vector Signal Analyzer and Software-Defined Receiver. Goel, A., +, TMTT May 2012 1375-1389 Interference suppression Miniaturized UWB Filters Integrated With Tunable Notch Filters Using a Silicon-Based Integrated Passive Device Technology. Wu, Z., +, TMTT March 2012 518-527 Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Intermodulation Novel MMIC Power Amplifier Linearization Utilizing Input Reflected Nonlinearity. Kuo, N.-C., +, TMTT March 2012 542-554 Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes. Suarez, A., +, TMTT March 2012 528-541 + Check author entry for coauthors

Intermodulation distortion 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 Direct Baseband I-Q Regeneration Method for Five-Port Receivers Improving DC-Offset and Second-Order Intermodulation Distortion Rejection. de la Morena-Alvarez-Palencia, C., +, TMTT Aug. 2012 2634-2643 Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links. Alcaro, G., +, TMTT Jan. 2012 185-194 Robust Analog Canceller for High-Dynamic-Range Radio Frequency Measurement. Wetherington, J. M., +, TMTT June 2012 1709-1719 Intermodulation measurement Robust Analog Canceller for High-Dynamic-Range Radio Frequency Measurement. Wetherington, J. M., +, TMTT June 2012 1709-1719 Interpolation Interpolation-Based Parameterized Model Order Reduction of Delayed Systems. Ferranti, F., +, TMTT March 2012 431-440 Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach. Kabir, M., +, TMTT Dec. 2012 3927-3938 Inverse problems Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation. Kilic, E., +, TMTT May 2012 14371443 Inverters A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the Turnstile Waveguide Circulator. Helszajn, J., +, TMTT Oct. 2012 3079-3087 Comments on "Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter". Sun, Z., +, TMTT Sept. 2012 2934 GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion. Garcia, J. A., +, TMTT Dec. 2012 4220-4229 Isolation technology A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module. Suga, R., +, TMTT March 2012 640-646 Iterative methods A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Longitudinal-Partitioning-Based Waveform Relaxation Algorithm for Efficient Analysis of Distributed Transmission-Line Networks. Roy, S., +, TMTT March 2012 451-463 Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation. Kilic, E., +, TMTT May 2012 14371443 Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay. Zhang, Q., +, TMTT Aug. 2012 2394-2402

J Jacobian matrices Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures. Dadash, M. S., +, TMTT Sept. 2012 2713-2722 Jitter An 8-bit Integrate-and-Sample Receiver for Rate-Scalable Photonic Analog-to-Digital Conversion. Gathman, T. D., +, TMTT Dec. 2012 3798-3809

K Kalman filters Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM. Zong, Z.-Y., +, TMTT June 2012 1500-1512 Klystrons Nonperiodic Perturbations in Periodic RF Structures. Jabotinski, V., +, TMTT April 2012 915-929 Kramers-Kronig relations Comments on "A Unique Extraction of Metamaterial Parameters Based on Kramers-Kronig Relationship". Barroso, J. J., +, TMTT June 2012 17431744

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L Ladder networks Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay. Zhang, Q., +, TMTT Aug. 2012 2394-2402 Laser beam machining Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Lattice networks Generalized Lattice Network-Based Balanced Composite Right-/LeftHanded Transmission Lines. Esteban, J., +, TMTT Aug. 2012 2385-2393 Layout Coupled Line 180 Hybrids With Lange Couplers. Napijalo, V., +, TMTT Dec. 2012 3674-3682 Wideband Dual-Mode Microstrip Filter Using Short-Ended Resonator With Centrally Loaded Inductive Stub. Sun, S.-J., +, TMTT Dec. 2012 3667-3673 LC circuits and A Generalized Dual-Band Wilkinson Power Divider With Parallel Components. Wang, X., +, TMTT April 2012 952-964 Leakage currents 60-GHz Dual-Conversion Down-/Up-Converters Using Schottky Diode in 0.18 m Foundry CMOS Technology. Wei, H.-J., +, TMTT June 2012 16841698 Leaky wave antennas Ring-Resonator-Inspired Power Recycling Scheme for Gain-Enhanced Distributed Amplifier-Based CRLH-Transmission Line Leaky Wave Antennas. Wu, C.-T. M., +, TMTT April 2012 1027-1037 Learning systems Peak-Power Controlled Digital Predistorters for RF Power Amplifiers. Landin, P. N., +, TMTT Nov. 2012 3582-3590 Least mean squares methods Optimized Low-Complexity Implementation of Least Squares Based Model Extraction for Digital Predistortion of RF Power Amplifiers. Guan, L., +, TMTT March 2012 594-603 Least squares approximations An Instrumental Variable Vector-Fitting Approach for Noisy Frequency Responses. Beygi, A., +, TMTT Sept. 2012 2702-2712 Complex-Chebyshev Functional Link Neural Network Behavioral Model for Broadband Wireless Power Amplifiers. Li, M., +, TMTT June 2012 1979-1989 Formulation for Complete and Accurate Calibration of Six-Port Reflectometer. Haddadi, K., +, TMTT March 2012 574-581 Modified Least Squares Extraction for Volterra-Series Digital Predistorter in the Presence of Feedback Measurement Errors. Liu, Y.-J., +, TMTT Nov. 2012 3559-3570 Lens antennas A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 Linear network analysis Graphical Analysis of Stabilization Loss and Gains for Three-Port Networks. Tan, E. L., +, TMTT June 2012 1635-1640 Robust Passive Macro-Model Generation With Local Compensation. Wang, T., +, TMTT Aug. 2012 2313-2328 Linearity High-Gain and High-Efficiency EER/Polar Transmitters Using InjectionLocked Oscillators. Chen, C.-T., +, TMTT Dec. 2012 4117-4128 PA Efficiency and Linearity Enhancement Using External Harmonic Injection. Dani, A., +, TMTT Dec. 2012 4097-4106 Linearization techniques A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490 Millimeter-Wave Self-Healing Power Amplifier With Adaptive Amplitude and Phase Linearization in 65-nm CMOS. Liu, J. Y.-C., +, TMTT May 2012 1342-1352 Liquid crystal polymers A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 Cascaded Coupled Line Filter With Reconfigurable Bandwidths Using LCP Multilayer Circuit Technology. Miller, A., +, TMTT June 2012 1577-1586 Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology. Qian, S., +, TMTT Sept. 2012 2799-2807 + Check author entry for coauthors

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Liquid crystals A 2-D Electronically Steered Phased-Array Antenna With 2 2 Elements in LC Display Technology. Karabey, O. H., +, TMTT May 2012 1297-1306 Liquids Accurate Nanoliter Liquid Characterization Up to 40 GHz for Biomedical Applications: Toward Noninvasive Living Cells Monitoring. Chen, T., +, TMTT Dec. 2012 4171-4177 Lithium compounds Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Logic gates 4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers. Aja Abelan, B., +, TMTT Dec. 2012 4080-4088 A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN. Chen, J.-H., +, TMTT Dec. 2012 4089-4096 CMOS Integrated Antenna-Coupled Field-Effect Transistors for the Detection of Radiation From 0.2 to 4.3 THz. Boppel, S., +, TMTT Dec. 2012 3834-3843 GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion. Garcia, J. A., +, TMTT Dec. 2012 4220-4229 Multiphysics Modeling of RF and Microwave High-Power Transistors. Aaen, P. H., +, TMTT Dec. 2012 4013-4023 Resistive Graphene FET Subharmonic Mixers: Noise and Linearity Assessment. Andersson, M. A., +, TMTT Dec. 2012 4035-4042 Long Term Evolution A Fully Integrated Watt-Level Linear 900-MHz CMOS RF Power Amplifier for LTE-Applications. Francois, B., +, TMTT June 2012 1878-1885 A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications. Hassan, M., +, TMTT May 2012 1321-1330 Analysis and Design of a Stacked Power Amplifier With Very High Bandwidth. Fritsche, D., +, TMTT Oct. 2012 3223-3231 Analysis and Implementation of Doherty Power Amplifier With Two-Point Envelope Modulation. Kim, J. H., +, TMTT May 2012 1353-1364 Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier. Saad, P., +, TMTT June 2012 1840-1849 Single-Chip Multiband EGPRS and SAW-Less LTE WCDMA CMOS Receiver With Diversity. Xie, H., +, TMTT May 2012 1390-1396 Losses A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 High-Performance Solenoidal RF Transformers on High-Resistivity Silicon Substrates for 3D Integrated Circuits. Feng, Z., +, TMTT July 2012 20662072 Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates. Evseev, S. B., +, TMTT Nov. 2012 3542-3550 Ultra-Wideband Single and Dual Baluns Based on Substrate Integrated Coaxial Line Technology. Zhu, F., +, TMTT Oct. 2012 3062-3070 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Low noise amplifiers -Band Total Power Radiometer Performance Optimization in an SiGe HBT Technology. Dacquay, E., +, TMTT March 2012 813-826 0.6–3-GHz Wideband Receiver RF Front-End With a Feedforward Noise and Distortion Cancellation Resistive-Feedback LNA. Wang, X., +, TMTT Feb. 2012 387-392 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 A Wideband Low-Power CMOS LNA With Positive–Negative Feedback for Noise, Gain, and Linearity Optimization. Woo, S., +, TMTT Oct. 2012 3169-3178 Analysis and Design of a 60 GHz Wideband Voltage-Voltage Transformer Feedback LNA. Sakian, P., +, TMTT March 2012 702-713

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Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467 Design and Analysis of a 21–29-GHz Ultra-Wideband Receiver Front-End in 0.18- m CMOS Technology. Lin, Y.-S., +, TMTT Aug. 2012 2590-2604 Design and Analysis of a Low-Power 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance. Uzunkol, M., +, TMTT Oct. 2012 32633271 ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process. Lin, C.-Y., +, TMTT March 2012 714-723 Low-Power Sub-Harmonic Direct-Conversion Receiver With Tunable RF LNA and Wideband LO Generator at U-NII Bands. Syu, J.-S., +, TMTT March 2012 555-566 Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 Parasitic-Insensitive Linearization Methods for 60-GHz 90-nm CMOS LNAs. Li, W.-T., +, TMTT Aug. 2012 2512-2523 Single-Chip Multiband EGPRS and SAW-Less LTE WCDMA CMOS Receiver With Diversity. Xie, H., +, TMTT May 2012 1390-1396 Subharmonic 220- and 320-GHz SiGe HBT Receiver Front-Ends. Ojefors, E., +, TMTT May 2012 1397-1404 Wideband CMOS Amplification Stage for a Direct-Sampling Square Kilometre Array Receiver. Navaratne, D., +, TMTT Oct. 2012 3179-3188 Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078 Low-pass filters A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading. Koswatta, R. V., +, TMTT Sept. 2012 2925-2933 Comments on “Theoretical and Experimental Study of a New Class of Reflectionless Filter”. Roy, S. C. D., +, TMTT March 2012 632-633 Formal Expression of Sensitivity and Energy Relationship in the Context of the Coupling Matrix. Martinez-Mendoza, M., +, TMTT Nov. 2012 33693375 Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay. Zhang, Q., +, TMTT Aug. 2012 2394-2402 Low-power electronics -Band CMOS Differential and Quadrature Voltage-Controlled Oscillators for Low Phase-Noise and Low-Power Applications. Chang, H.-Y., +, TMTT Jan. 2012 46-59 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator. Lee, S., +, TMTT May 2012 1405-1412 A 1.1-V Regulator-Stabilized 21.4-GHz VCO and a 115% Frequency-Range Dynamic Divider for -Band Wireless Communication. Nakamura, T., +, TMTT Sept. 2012 2823-2832 A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 A CMOS Distributed Amplifier With Distributed Active Input Balun Using GBW and Linearity Enhancing Techniques. Jahanian, A., +, TMTT May 2012 1331-1341 A Highly Reconfigurable Low-Power CMOS Directional Coupler. Sun, J., +, TMTT Sept. 2012 2815-2822 A Low-Voltage, Low-Power, and Low-Noise UWB Mixer Using Bulk-Injection and Switched Biasing Techniques. Kim, M.-G., +, TMTT Aug. 2012 2486-2493 A Wideband Low-Power CMOS LNA With Positive–Negative Feedback for Noise, Gain, and Linearity Optimization. Woo, S., +, TMTT Oct. 2012 3169-3178 An Ultra-Low-Voltage and Low-Power 2 Subharmonic Downconverter Mixer. He, S., +, TMTT Feb. 2012 311-317 Design and Analysis of a -band Divide-by-Three Injection-Locked Frequency Divider Using Second Harmonic Enhancement Technique. Yeh, Y.-L., +, TMTT June 2012 1617-1625 Design and Analysis of a Low-Power 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance. Uzunkol, M., +, TMTT Oct. 2012 32633271 Design of 40–108-GHz Low-Power and High-Speed CMOS Up-/DownConversion Ring Mixers for Multistandard MMW Radio Applications. Tsai, J.-H., +, TMTT March 2012 670-678 Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 + Check author entry for coauthors

Low-Power Wireless Power Delivery. Falkenstein, E., +, TMTT July 2012 2277-2286 Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Low-Voltage, Wide-Locking-Range, Millimeter-Wave Divide-by-5 Injection-Locked Frequency Dividers. Li, M.-W., +, TMTT March 2012 679-685 Pulse-Biased Low-Power Low-Phase-Noise UHF LC-QVCO for 866 MHz RFID Front-End. Li, J., +, TMTT Oct. 2012 3120-3125 Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Lumped parameter networks High-Performance Solenoidal RF Transformers on High-Resistivity Silicon Substrates for 3D Integrated Circuits. Feng, Z., +, TMTT July 2012 20662072 Longitudinal-Partitioning-Based Waveform Relaxation Algorithm for Efficient Analysis of Distributed Transmission-Line Networks. Roy, S., +, TMTT March 2012 451-463 Lumped-Element Realization of Absorptive Bandstop Filter With Anomalously High Spectral Isolation. Lee, J., +, TMTT Aug. 2012 2424-2430 Lyapunov methods Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes. Suarez, A., +, TMTT March 2012 528-541

M

Magnetic flux Theory of Magnetic Transmission Lines. Brandao Faria, J. A., +, TMTT Oct. 2012 2941-2949 Magnetic resonance Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave. Wu, J., +, TMTT Dec. 2012 3959-3968 Magnetoelectric effects Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 Magnetostatic waves Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave. Wu, J., +, TMTT Dec. 2012 3959-3968 Magnetostatics Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave. Wu, J., +, TMTT Dec. 2012 3959-3968 Mathematical analysis Controlling Active Load–Pull in a Dual-Input Inverse Load Modulated Doherty Architecture. Hone, T. M., +, TMTT June 2012 1797-1804 Low-Frequency Noise Sources and Gain Stability in Microwave Amplifiers for Radiometry. Gonneau, E., +, TMTT Aug. 2012 2616-2621 Mathematical model A Unified Theory for -Parameter Uncertainty Evaluation. Garelli, M., +, TMTT Dec. 2012 3844-3855 Analysis and Design of Low Phase-Noise Oscillators With Nonlinear Resonators. Imani, A., +, TMTT Dec. 2012 3749-3760 Coupled Line 180 Hybrids With Lange Couplers. Napijalo, V., +, TMTT Dec. 2012 3674-3682 Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides. Ochoa, J. S., +, TMTT Dec. 2012 3919-3926 FDTD Modeling of Impedance Boundary Conditions by Equivalent LTI Circuits. Feliziani, M., +, TMTT Dec. 2012 3656-3666 Generalization and Reduction of Line-Series-Shunt Calibration for Broadband GaAs and CMOS On-Wafer Scattering Parameter Measurements. Huang, C.-C., +, TMTT Dec. 2012 4138-4144 Passive Subharmonic Generation Using Memoryless Nonlinear Circuits. Safarian, Z., +, TMTT Dec. 2012 4053-4065 Mathematics computing MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit. De Donno, D., +, TMTT Sept. 2012 2693-2701 Matrix algebra A 0.01–8-GHz (12.5 Gb/s) 4 4 CMOS Switch Matrix. Shin, D., +, TMTT Feb. 2012 381-386

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 Analytical Design of Two-Mode Dual-Band Filters Using E-Shaped Resonators. Kuo, Y.-T., +, TMTT Feb. 2012 250-260 Efficient Analysis of Metallic and Dielectric Posts in Parallel-Plate Waveguide Structures. Casaletti, M., +, TMTT Oct. 2012 2979-2989 Formal Expression of Sensitivity and Energy Relationship in the Context of the Coupling Matrix. Martinez-Mendoza, M., +, TMTT Nov. 2012 33693375 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control. Serrano, A. L. C., +, TMTT March 2012 484-493 Maxwell equations A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures. Dadash, M. S., +, TMTT Sept. 2012 2713-2722 In Vitro Dosimetry and Temperature Evaluations of a Typical MillimeterWave Aperture-Field Exposure Setup. Zhao, J., +, TMTT Nov. 2012 36083622 On the Equivalence Between the Maxwell-Garnett Mixing Rule and the Debye Relaxation Formula. Salski, B., +, TMTT Aug. 2012 2352-2358 SPICE Lumped Circuit Subcell Model for the Discontinuous Galerkin Finite-Element Time-Domain Method. Zhao, B., +, TMTT Sept. 2012 26842692 Theoretical Design and Analysis for – Rectangular Waveguide Mode Converters. Zhang, Q., +, TMTT April 2012 1018-1026 TLM Extension to Electromagnetic Field Analysis of Anisotropic and Dispersive Media: A Unified Field Equation. Farhat, A. L., +, TMTT Aug. 2012 2339-2351 Mean square error methods A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array. Kim, C.-Y., +, TMTT March 2012 730-742 A Full 360 Vector-Sum Phase Shifter With Very Low RMS Phase Error Over a Wide Bandwidth. Asoodeh, A., +, TMTT June 2012 1626-1634 An Open-Loop Half-Quadrature Hybrid for Multiphase Signals Generation. Chen, H.-S., +, TMTT Jan. 2012 131-138 Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 Digital Predistortion for High Efficiency Power Amplifier Architectures Using a Dual-Input Modeling Approach. Cao, H., +, TMTT Feb. 2012 361-369 Subsampling Feedback Loop Applicable to Concurrent Dual-Band Linearization Architecture. Bassam, S. A., +, TMTT June 2012 1990-1999 Measurement errors 16-Term Error Model in Reciprocal Systems. Silvonen, K., +, TMTT Nov. 2012 3551-3558 Device Characterization Techniques Based on Causal Relationships. Wojnowski, M., +, TMTT July 2012 2203-2219 Measurement systems Terahertz Micromachined On-Wafer Probes: Repeatability and Reliability. Chen, L., +, TMTT Sept. 2012 2894-2902 Measurement uncertainty A Unified Theory for -Parameter Uncertainty Evaluation. Garelli, M., +, TMTT Dec. 2012 3844-3855 Simple Test and Modeling of RFID Tag Backscatter. Kuester, D. G., +, TMTT July 2012 2248-2258 Meetings 2011 RFIC Symposium Mini-Special Issue Editorial. Ponchak, G. E., +, TMTT May 2012 1185 Guest Editorial. Lin, F., +, TMTT Nov. 2012 3347-3348 Metallization Design and Analysis of Down-Conversion Gate/Base-Pumped Harmonic Mixers Using Novel Reduced-Size 180 Hybrid With Different Input Frequencies. Kuo, J.-J., +, TMTT Aug. 2012 2473-2485

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Millimeter-Wave Printed Circuit Board Characterization Using Substrate Integrated Waveguide Resonators. Zelenchuk, D. E., +, TMTT Oct. 2012 3300-3308 Metals Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range. Voinigescu, S. P., +, TMTT Dec. 2012 4024-4034 Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings. Memarian, M., +, TMTT Dec. 2012 3893-3907 Metamaterial antennas Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Metamaterials Analysis of Composite Right/Left-Handed Unit Cells Based on Even–OddMode Excitation. Eberspacher, M. A., +, TMTT May 2012 1186-1196 Authors’ Reply to “Comments on Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship”. Szabo, Z., +, TMTT Nov. 2012 3634-3635 Comments on "A Unique Extraction of Metamaterial Parameters Based on Kramers-Kronig Relationship". Barroso, J. J., +, TMTT June 2012 17431744 Dual Composite Right-/Left-Handed Coplanar Waveguide Transmission Line Using Inductively Connected Split-Ring Resonators. Belenguer, A., +, TMTT Oct. 2012 3035-3042 Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies. Bayatpur, F., +, TMTT April 2012 1126-1135 Generalized Lattice Network-Based Balanced Composite Right-/LeftHanded Transmission Lines. Esteban, J., +, TMTT Aug. 2012 2385-2393 Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Polarization-Independent Metamaterial Analog of Electromagnetically Induced Transparency for a Refractive-Index-Based Sensor. Meng, F.-Y., +, TMTT Oct. 2012 3013-3022 Pseudo-Traveling-Wave Resonator With Magnetically Tunable Phase Gradient of Fields and Its Applications to Beam-Steering Antennas. Ueda, T., +, TMTT Oct. 2012 3043-3054 Ring-Resonator-Inspired Power Recycling Scheme for Gain-Enhanced Distributed Amplifier-Based CRLH-Transmission Line Leaky Wave Antennas. Wu, C.-T. M., +, TMTT April 2012 1027-1037 Method of moments Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures. Dadash, M. S., +, TMTT Sept. 2012 2713-2722 MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit. De Donno, D., +, TMTT Sept. 2012 2693-2701 MHEMTs 4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers. Aja Abelan, B., +, TMTT Dec. 2012 4080-4088 Micromachining A -Band Micromachined 3-D Cavity-Backed Patch Antenna Array With Integrated Diode Detector. Oliver, J. M., +, TMTT Feb. 2012 284-292 A High-Performance Continuously Tunable MEMS Bandpass Filter at 1 GHz. Shim, Y., +, TMTT Aug. 2012 2439-2447 Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Micromechanical devices A High-Performance Continuously Tunable MEMS Bandpass Filter at 1 GHz. Shim, Y., +, TMTT Aug. 2012 2439-2447 Power Handling of Electrostatic MEMS Evanescent-Mode (EVA) Tunable Bandpass Filters. Liu, X., +, TMTT Feb. 2012 270-283 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Micromechanical resonators A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 Microrelays An All-Metal Micro-Relay With Bulk Foil Pt–Rh Contacts for High-Power RF Applications. Ozkeskin, F. M., +, TMTT June 2012 1595-1604 Microscopy Performance Limitations and Measurement Analysis of a Near-Field Microwave Microscope for Nondestructive and Subsurface Detection. Chisum, J. D., +, TMTT Aug. 2012 2605-2615

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Microstrip An Ultra-Thin, High-Power, and Multilayer Organic Antenna Array With T/R Functionality in the -Band. Donado Morcillo, C. A., +, TMTT Dec. 2012 3856-3867 Microstrip antenna arrays A -Band Micromachined 3-D Cavity-Backed Patch Antenna Array With Integrated Diode Detector. Oliver, J. M., +, TMTT Feb. 2012 284-292 Microstrip antennas A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Microstrip circuits A Broadband and Vialess Vertical Microstrip-to-Microstrip Transition. Huang, X., +, TMTT April 2012 938-944 Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter. Lin, F., +, TMTT May 2012 1226-1234 MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit. De Donno, D., +, TMTT Sept. 2012 2693-2701 Microstrip components A Fully Symmetrical Crossover and Its Dual-Frequency Application. Shao, J., +, TMTT Aug. 2012 2410-2416 Self-Biased Nonreciprocal Microstrip Phase Shifter on Magnetic Nanowired Substrate Suitable for Gyrator Applications. Hamoir, G., +, TMTT July 2012 2152-2157 Microstrip couplers A Rigorous Design Methodology for Compact Planar Branch-Line and RatRace Couplers With Asymmetrical T-Structures. Tseng, C.-H., +, TMTT July 2012 2085-2092 Quasi-Arbitrary Phase-Difference Hybrid Coupler. Wong, Y. S., +, TMTT June 2012 1530-1539 Simulation and Experiment of a Compact Wideband 90 Differential Phase Shifter. Sorn, M., +, TMTT March 2012 494-501 Microstrip filters A Quasi Elliptic Function 1.75–2.25 GHz 3-Pole Bandpass Filter With Bandwidth Control. Chiou, Y.-C., +, TMTT Feb. 2012 244-249 A Tunable Combline Bandpass Filter Loaded With Series Resonator. Wang, X.-G., +, TMTT June 2012 1569-1576 Design Method for Ultra-Wideband Bandpass Filter With Wide Stopband Using Parallel-Coupled Microstrip Lines. Abbosh, A. M., +, TMTT Jan. 2012 31-38 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Intrinsically Switched Varactor-Tuned Filters and Filter Banks. Guyette, A. C., +, TMTT April 2012 1044-1056 Microstrip Bandpass Filters With Various Resonators Using Connected- and Edge-Coupling Mechanisms and Their Applications to Dual-Band Filters and Diplexers. Lin, S.-C., +, TMTT April 2012 975-988 Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology. Qian, S., +, TMTT Sept. 2012 2799-2807 Novel Second-Order Dual-Mode Dual-Band Filters Using Capacitance Loaded Square Loop Resonator. Fu, S., +, TMTT March 2012 477-483 Phase Velocities Equalization of Coupled Microstrip Lines Using -Shaped Particles and Suppression of the Second Harmonic. Hatefi Ardakani, H., +, TMTT March 2012 464-470 Stepped-Impedance Coupled Resonators for Implementation of Parallel Coupled Microstrip Filters With Spurious Band Suppression. Worapishet, A., +, TMTT June 2012 1540-1548 Microstrip lines A 17–35 GHz Broadband, High Efficiency PHEMT Power Amplifier Using Synthesized Transformer Matching Technique. Huang, P.-C., +, TMTT Jan. 2012 112-119 A Broadband U-Slot Coupled Microstrip-to-Waveguide Transition. Huang, X., +, TMTT May 2012 1210-1217 A Directivity-Enhanced Directional Coupler Using Epsilon Negative Transmission Line. Pourzadi, A., +, TMTT Nov. 2012 3395-3402 A High Slow-Wave Factor Microstrip Structure With Simple Design Formulas and Its Application to Microwave Circuit Design. Chang, W.-S., +, TMTT Nov. 2012 3376-3383 A New High-Efficient Spectral-Domain Analysis of Single and Multiple Coupled Microstrip Lines in Planarly Layered Media. Lucido, M., +, TMTT July 2012 2025-2034

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A Rigorous Design Methodology for Compact Planar Branch-Line and RatRace Couplers With Asymmetrical T-Structures. Tseng, C.-H., +, TMTT July 2012 2085-2092 A Temperature-Compensation Technique for Substrate Integrated Waveguide Cavities and Filters. Djerafi, T., +, TMTT Aug. 2012 2448-2455 Comments on "Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter". Sun, Z., +, TMTT Sept. 2012 2934 Common-Mode Suppression in Microstrip Differential Lines by Means of Complementary Split Ring Resonators: Theory and Applications. Naqui, J., +, TMTT Oct. 2012 3023-3034 Design Method for Ultra-Wideband Bandpass Filter With Wide Stopband Using Parallel-Coupled Microstrip Lines. Abbosh, A. M., +, TMTT Jan. 2012 31-38 Design of a New Type Planar Balun by Using Trans-Directional Couplers. Shie, C.-I., +, TMTT March 2012 471-476 Design of High-Order Wideband Planar Balun Filter in -Plane Bandpass Prototype. Lin, Y.-W., +, TMTT July 2012 2124-2130 Generalized Lattice Network-Based Balanced Composite Right-/LeftHanded Transmission Lines. Esteban, J., +, TMTT Aug. 2012 2385-2393 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 Phase Velocities Equalization of Coupled Microstrip Lines Using -Shaped Particles and Suppression of the Second Harmonic. Hatefi Ardakani, H., +, TMTT March 2012 464-470 Microstrip resonators A Broadband and Vialess Vertical Microstrip-to-Microstrip Transition. Huang, X., +, TMTT April 2012 938-944 Analytical Design of Two-Mode Dual-Band Filters Using E-Shaped Resonators. Kuo, Y.-T., +, TMTT Feb. 2012 250-260 Independence of the Unloaded of a Planar Electromagnetic Resonator From Its Shape. Naji, A., +, TMTT Aug. 2012 2370-2377 Microstrip transitions A Broadband and Vialess Vertical Microstrip-to-Microstrip Transition. Huang, X., +, TMTT April 2012 938-944 Microswitches A High-Reliability High-Linearity High-Power RF MEMS Metal-Contact Switch for DC–40-GHz Applications. Patel, C. D., +, TMTT Oct. 2012 3096-3112 Microwave amplifiers -Band Amplifiers With 6-dB Noise Figure and Milliwatt-Level 170–200-GHz Doublers in 45-nm CMOS. Cetinoneri, B., +, TMTT March 2012 692-701 A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490 Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467 Low-Frequency Noise Sources and Gain Stability in Microwave Amplifiers for Radiometry. Gonneau, E., +, TMTT Aug. 2012 2616-2621 Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide. Zhang, L., +, TMTT Jan. 2012 1-7 Power Amplification at 0.65 THz Using InP HEMTs. Radisic, V., +, TMTT March 2012 724-729 Microwave antenna arrays A -Band Micromachined 3-D Cavity-Backed Patch Antenna Array With Integrated Diode Detector. Oliver, J. M., +, TMTT Feb. 2012 284-292 The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration. Diehl, J. F., +, TMTT Jan. 2012 195-200 Microwave antennas Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 Microwave bipolar transistors Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology. Kuylenstierna, D., +, TMTT Nov. 2012 3420-3430 Microwave circuits A High Slow-Wave Factor Microstrip Structure With Simple Design Formulas and Its Application to Microwave Circuit Design. Chang, W.-S., +, TMTT Nov. 2012 3376-3383 High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers. Roberg, M., +, TMTT Dec. 2012 4043-4052

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Large-Signal Oscillator Design Procedure Utilizing Analytical -Parameters Closed-Form Expressions. Pelaez-Perez, A. M., +, TMTT Oct. 2012 3126-3136 Microwave circulators 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 Microwave detectors Microwave Chemical Sensing at Room Temperature Using an Overmoded Waveguide Design. Huang, Y.-T., +, TMTT Sept. 2012 2886-2893 Microwave devices A Fully Symmetrical Crossover and Its Dual-Frequency Application. Shao, J., +, TMTT Aug. 2012 2410-2416 A Self-Sustained Microwave System for Dielectric-Constant Measurement of Lossy Organic Liquids. Sekar, V., +, TMTT May 2012 1444-1455 Design of Transmission-Type th-Order Differentiators in Planar Microwave Technology. Chudzik, M., +, TMTT Nov. 2012 3384-3394 Microwave diodes Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467 Microwave and RF p-i-n Diode Model for Time-Domain Simulation. Caverly, R. H., +, TMTT July 2012 2158-2164 Novel Modeling and Calibration Approach for Multiport Receivers Mitigating System Imperfections and Hardware Impairments. Hasan, A., +, TMTT Aug. 2012 2644-2653 Microwave field effect transistors A 3-D Table-Based Method for Non-Quasi-Static Microwave FET Devices Modeling. Long, Y., +, TMTT Oct. 2012 3088-3095 Localized Rapid Heating by Low-Power Solid-State Microwave Drill. Meir, Y., +, TMTT Aug. 2012 2665-2672 Microwave filters A High-Performance Continuously Tunable MEMS Bandpass Filter at 1 GHz. Shim, Y., +, TMTT Aug. 2012 2439-2447 A Narrow-Passband and Frequency-Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT May 2012 1287-1296 A Spurious-Free Discontinuous Galerkin Time-Domain Method for the Accurate Modeling of Microwave Filters. Alvarez, J., +, TMTT Aug. 2012 2359-2369 A Temperature-Compensation Technique for Substrate Integrated Waveguide Cavities and Filters. Djerafi, T., +, TMTT Aug. 2012 2448-2455 A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 Extended Passband Bandstop Filter Cascade With Continuous 0.85–6.6-GHz Coverage. Naglich, E. J., +, TMTT Jan. 2012 21-30 Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network. Penaranda-Foix, F. L., +, TMTT Sept. 2012 2730-2740 Miniaturized UWB Filters Integrated With Tunable Notch Filters Using a Silicon-Based Integrated Passive Device Technology. Wu, Z., +, TMTT March 2012 518-527 On the Relation Between Stored Energy and Fabrication Tolerances in Microwave Filters. Martinez-Mendoza, M., +, TMTT July 2012 2131-2141 Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control. Serrano, A. L. C., +, TMTT March 2012 484-493 Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses. Arnedo, I., +, TMTT May 2012 1244-1257 Synthesis of Vertical Interdigital Filters Using Multilayered Technologies. Perigaud, A., +, TMTT April 2012 965-974 Microwave heating Localized Rapid Heating by Low-Power Solid-State Microwave Drill. Meir, Y., +, TMTT Aug. 2012 2665-2672 Microwave imaging Performance Limitations and Measurement Analysis of a Near-Field Microwave Microscope for Nondestructive and Subsurface Detection. Chisum, J. D., +, TMTT Aug. 2012 2605-2615 Microwave integrated circuits A 1.1-V Regulator-Stabilized 21.4-GHz VCO and a 115% Frequency-Range Dynamic Divider for -Band Wireless Communication. Nakamura, T., +, TMTT Sept. 2012 2823-2832

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High-Performance Solenoidal RF Transformers on High-Resistivity Silicon Substrates for 3D Integrated Circuits. Feng, Z., +, TMTT July 2012 20662072 Rigorous Derivation and Fast Solution of Spatial-Domain Green’s Functions for Uniaxial Anisotropic Multilayers Using Modified Fast Hankel Transform Method. Ding, P.-P., +, TMTT Feb. 2012 205-217 Microwave materials Nonperiodic Perturbations in Periodic RF Structures. Jabotinski, V., +, TMTT April 2012 915-929 Microwave measurement Fast Multiharmonic Active Load–Pull System With Waveform Measurement Capabilities. Thorsell, M., +, TMTT Jan. 2012 149-157 Modified Least Squares Extraction for Volterra-Series Digital Predistorter in the Presence of Feedback Measurement Errors. Liu, Y.-J., +, TMTT Nov. 2012 3559-3570 Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 Novel Coupling Structure for the Resonant Coaxial Probe. Rowe, D. J., +, TMTT June 2012 1699-1708 The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration. Diehl, J. F., +, TMTT Jan. 2012 195-200 Microwave mixers A Low-Voltage, Low-Power, and Low-Noise UWB Mixer Using Bulk-Injection and Switched Biasing Techniques. Kim, M.-G., +, TMTT Aug. 2012 2486-2493 An Analytical Formulation for Black Box Conversion Matrix Extraction. Kheirdoost, A., +, TMTT June 2012 1493-1499 An Ultra-Low-Voltage and Low-Power 2 Subharmonic Downconverter Mixer. He, S., +, TMTT Feb. 2012 311-317 Design and Analysis of a 21–29-GHz Ultra-Wideband Receiver Front-End in 0.18- m CMOS Technology. Lin, Y.-S., +, TMTT Aug. 2012 2590-2604 Design and Analysis of Down-Conversion Gate/Base-Pumped Harmonic Mixers Using Novel Reduced-Size 180 Hybrid With Different Input Frequencies. Kuo, J.-J., +, TMTT Aug. 2012 2473-2485 Microwave oscillators A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator. Lee, S., +, TMTT May 2012 1405-1412 A 1.1-V Regulator-Stabilized 21.4-GHz VCO and a 115% Frequency-Range Dynamic Divider for -Band Wireless Communication. Nakamura, T., +, TMTT Sept. 2012 2823-2832 Analysis of Oscillation Modes in Free-Running Ring Oscillators. de Cos, J., +, TMTT Oct. 2012 3137-3150 Analysis of the Locking Range of Rationally Synchronized Oscillators With High Reference Signal Power. Fernandez Garcia, M., +, TMTT Aug. 2012 2494-2504 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology. Kuylenstierna, D., +, TMTT Nov. 2012 3420-3430 Experimental Characterization of Oscillator Circuits for Reduced-Order Models. Umpierrez, P., +, TMTT Nov. 2012 3527-3541 Low-Voltage, Wide-Locking-Range, Millimeter-Wave Divide-by-5 Injection-Locked Frequency Dividers. Li, M.-W., +, TMTT March 2012 679-685 Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide. Zhang, L., +, TMTT Jan. 2012 1-7 Microwave phase shifters A Full 360 Vector-Sum Phase Shifter With Very Low RMS Phase Error Over a Wide Bandwidth. Asoodeh, A., +, TMTT June 2012 1626-1634 Compact Tunable Reflection Phase Shifters Using Short Section of Coupled Lines. Abbosh, A. M., +, TMTT Aug. 2012 2465-2472 Compact, Low-Loss, Wideband, and High-Power Handling Phase Shifters With Piezoelectric Transducer-Controlled Metallic Perturber. Wu, J., +, TMTT June 2012 1587-1594 Microwave photonics A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 Millimeter-Wave Optoelectronic Mixers Based on Uni-Traveling Carrier Photodiodes. Rouvalis, E., +, TMTT March 2012 686-691 Optical Modulation of Millimeter-Wave Beams Using a Semiconductor Substrate. Gallacher, T. F., +, TMTT July 2012 2301-2309

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The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration. Diehl, J. F., +, TMTT Jan. 2012 195-200 Microwave power amplifiers 3–3.6-GHz Wideband GaN Doherty Power Amplifier Exploiting Output Compensation Stages. Rubio, J. M., +, TMTT Aug. 2012 2543-2548 A 17–35 GHz Broadband, High Efficiency PHEMT Power Amplifier Using Synthesized Transformer Matching Technique. Huang, P.-C., +, TMTT Jan. 2012 112-119 A 5-Gb/s 2.1–2.2-GHz Bandpass Modulator for Switch-Mode Power Amplifier. Ostrovskyy, P., +, TMTT Aug. 2012 2524-2531 Modified Least Squares Extraction for Volterra-Series Digital Predistorter in the Presence of Feedback Measurement Errors. Liu, Y.-J., +, TMTT Nov. 2012 3559-3570 Switching Behavior of Class-E Power Amplifier and Its Operation Above Maximum Frequency. Jee, S., +, TMTT Jan. 2012 89-98 Microwave propagation Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures. Dadash, M. S., +, TMTT Sept. 2012 2713-2722 Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses. Arnedo, I., +, TMTT May 2012 1244-1257 Microwave receivers 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 Novel Modeling and Calibration Approach for Multiport Receivers Mitigating System Imperfections and Hardware Impairments. Hasan, A., +, TMTT Aug. 2012 2644-2653 Microwave reflectometry Formulation for Complete and Accurate Calibration of Six-Port Reflectometer. Haddadi, K., +, TMTT March 2012 574-581 Microwave resonators A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 A High-Performance Continuously Tunable MEMS Bandpass Filter at 1 GHz. Shim, Y., +, TMTT Aug. 2012 2439-2447 Crosstalk Reduction for Superconducting Microwave Resonator Arrays. Noroozian, O., +, TMTT May 2012 1235-1243 Independence of the Unloaded of a Planar Electromagnetic Resonator From Its Shape. Naji, A., +, TMTT Aug. 2012 2370-2377 Microwave switches A 0.01–8-GHz (12.5 Gb/s) 4 4 CMOS Switch Matrix. Shin, D., +, TMTT Feb. 2012 381-386 A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 A High-Reliability High-Linearity High-Power RF MEMS Metal-Contact Switch for DC–40-GHz Applications. Patel, C. D., +, TMTT Oct. 2012 3096-3112 Analysis and Design of 60-GHz SPDT Switch in 130-nm CMOS. He, J., +, TMTT Oct. 2012 3113-3119 Prediction of Multipactor Breakdown for Multicarrier Applications: The Quasi-Stationary Method. Anza, S., +, TMTT July 2012 2093-2105 Microwave technology Gyrotropy and Nonreciprocity of Graphene for Microwave Applications. Sounas, D. L., +, TMTT April 2012 901-914 Microwave theory and techniques Accurate Nanoliter Liquid Characterization Up to 40 GHz for Biomedical Applications: Toward Noninvasive Living Cells Monitoring. Chen, T., +, TMTT Dec. 2012 4171-4177 Microwave transistors A 0.01–8-GHz (12.5 Gb/s) 4 4 CMOS Switch Matrix. Shin, D., +, TMTT Feb. 2012 381-386 A 17–35 GHz Broadband, High Efficiency PHEMT Power Amplifier Using Synthesized Transformer Matching Technique. Huang, P.-C., +, TMTT Jan. 2012 112-119 A Low-Voltage, Low-Power, and Low-Noise UWB Mixer Using Bulk-Injection and Switched Biasing Techniques. Kim, M.-G., +, TMTT Aug. 2012 2486-2493 Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467

+ Check author entry for coauthors

High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers. Roberg, M., +, TMTT Dec. 2012 4043-4052 Switching Behavior of Class-E Power Amplifier and Its Operation Above Maximum Frequency. Jee, S., +, TMTT Jan. 2012 89-98 Millimeter wave amplifiers -Band Amplifiers With 6-dB Noise Figure and Milliwatt-Level 170–200-GHz Doublers in 45-nm CMOS. Cetinoneri, B., +, TMTT March 2012 692-701 A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Design and Analysis of a Low-Power 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance. Uzunkol, M., +, TMTT Oct. 2012 32633271 Design-in-Reliable Millimeter-Wave Power Amplifiers in a 65-nm CMOS Process. Quemerais, T., +, TMTT April 2012 1079-1085 ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process. Lin, C.-Y., +, TMTT March 2012 714-723 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 Gain-Bandwidth Analysis of Broadband Darlington Amplifiers in HBT-HEMT Process. Weng, S.-H., +, TMTT Nov. 2012 3458-3473 Parasitic-Insensitive Linearization Methods for 60-GHz 90-nm CMOS LNAs. Li, W.-T., +, TMTT Aug. 2012 2512-2523 Power Amplification at 0.65 THz Using InP HEMTs. Radisic, V., +, TMTT March 2012 724-729 Millimeter wave antenna arrays A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 Millimeter wave antennas Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 New Method for Determining Dielectric Properties of Skin and Phantoms at Millimeter Waves Based on Heating Kinetics. Chahat, N., +, TMTT March 2012 827-832 Optical Modulation of Millimeter-Wave Beams Using a Semiconductor Substrate. Gallacher, T. F., +, TMTT July 2012 2301-2309 Millimeter wave bipolar transistors A Transformer-Coupling Current-Reuse SiGe HBT Power Amplifier for 77-GHz Automotive Radar. Giammello, V., +, TMTT June 2012 1676-1683 Gain-Bandwidth Analysis of Broadband Darlington Amplifiers in HBT-HEMT Process. Weng, S.-H., +, TMTT Nov. 2012 3458-3473 Systematic Compact Modeling of Correlated Noise in Bipolar Transistors. Herricht, J., +, TMTT Nov. 2012 3403-3412 Millimeter wave circuits Guest Editorial. Rebeiz, G. M., +, TMTT March 2012 637-639 Millimeter wave devices Ultrafast Low-Loss 42–70 GHz Differential SPDT Switch in 0.35 m SiGe Technology. Thian, M., +, TMTT March 2012 655-659 Millimeter wave diodes Broadband Millimeter-Wave Single Balanced Mixer and Its Applications to Substrate Integrated Wireless Systems. Zhang, Z.-Y., +, TMTT March 2012 660-669 Millimeter wave directional couplers A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Millimeter wave filters Design and Analysis of a Tri-Band Dual-Mode Chip Filter for 60-, 77-, and 100-GHz Applications. Yang, C.-L., +, TMTT April 2012 989-997 Millimeter wave frequency converters Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Millimeter wave generation Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation. Jooyaie, A., +, TMTT Aug. 2012 2505-2511 Millimeter wave integrated circuits 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission. Hirata, A., +, TMTT March 2012 881-895

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Analysis and Design of 60-GHz SPDT Switch in 130-nm CMOS. He, J., +, TMTT Oct. 2012 3113-3119 Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators. Gupta, A. K., +, TMTT Oct. 2012 3272-3285 Vertical RF Transition With Mechanical Fit for 3-D Heterogeneous Integration. Chen, L., +, TMTT March 2012 647-654 Millimeter wave mixers Broadband Millimeter-Wave Single Balanced Mixer and Its Applications to Substrate Integrated Wireless Systems. Zhang, Z.-Y., +, TMTT March 2012 660-669 Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes. Rouvalis, E., +, TMTT March 2012 509-517 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Millimeter-Wave Optoelectronic Mixers Based on Uni-Traveling Carrier Photodiodes. Rouvalis, E., +, TMTT March 2012 686-691 Millimeter wave oscillators A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Low-Voltage, Wide-Locking-Range, Millimeter-Wave Divide-by-5 Injection-Locked Frequency Dividers. Li, M.-W., +, TMTT March 2012 679-685 Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation. Jooyaie, A., +, TMTT Aug. 2012 2505-2511 Millimeter wave phase shifters An Improved Wideband All-Pass I/Q Network for Millimeter-Wave Phase Shifters. Kim, S. Y., +, TMTT Nov. 2012 3431-3439 Millimeter wave power amplifiers -Band and -Band Power Amplifiers in 45-nm CMOS SOI. Kim, J., +, TMTT June 2012 1870-1877 A Compact Linear 60-GHz PA With 29.2% PAE Operating at Weak Avalanche Area in SiGe. Sun, Y., +, TMTT Aug. 2012 2581-2589 A Nested-Reactance Feedback Power Amplifier for -Band Applications. Kalantari, N., +, TMTT June 2012 1667-1675 A Transformer-Coupling Current-Reuse SiGe HBT Power Amplifier for 77-GHz Automotive Radar. Giammello, V., +, TMTT June 2012 1676-1683 Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators. Gupta, A. K., +, TMTT Oct. 2012 3272-3285 Millimeter-Wave Self-Healing Power Amplifier With Adaptive Amplitude and Phase Linearization in 65-nm CMOS. Liu, J. Y.-C., +, TMTT May 2012 1342-1352 Millimeter wave propagation Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 Millimeter wave radar 24-GHz Integrated Radio and Radar System Capable of Time-Agile Wireless Communication and Sensing. Han, L., +, TMTT March 2012 619-631 Millimeter-Wave Technology for Automotive Radar Sensors in the 77 GHz Frequency Band. Hasch, J., +, TMTT March 2012 845-860 Security Pre-screening of Moving Persons Using a Rotating Multichannel -Band Radar. Hantscher, S., +, TMTT March 2012 870-880 Millimeter wave receivers Design and Analysis of a Low-Power 3–6-Gb/s 55-GHz OOK Receiver With High-Temperature Performance. Uzunkol, M., +, TMTT Oct. 2012 32633271 Millimeter wave resonators Millimeter-Wave Printed Circuit Board Characterization Using Substrate Integrated Waveguide Resonators. Zelenchuk, D. E., +, TMTT Oct. 2012 3300-3308 Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation. Jooyaie, A., +, TMTT Aug. 2012 2505-2511 Millimeter wave technology Guest Editorial. Rebeiz, G. M., +, TMTT March 2012 637-639 + Check author entry for coauthors

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Millimeter waves In Vitro Dosimetry and Temperature Evaluations of a Typical MillimeterWave Aperture-Field Exposure Setup. Zhao, J., +, TMTT Nov. 2012 36083622 MIMO communication 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 A Single Envelope Modulator-Based Envelope-Tracking Structure for Multiple-Input and Multiple-Output Wireless Transmitters. Yu, C., +, TMTT Oct. 2012 3317-3327 Minimum shift keying A Broadband Injection-Locking Class-E Power Amplifier. Lin, C.-H., +, TMTT Oct. 2012 3232-3242 Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks. Cantu, H. I., +, TMTT Sept. 2012 2903-2912 MISFET Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates. Evseev, S. B., +, TMTT Nov. 2012 3542-3550 Mixers (circuits) 245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology. Mao, Y., +, TMTT Dec. 2012 3823-3833 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading. Koswatta, R. V., +, TMTT Sept. 2012 2925-2933 An Open-Loop Half-Quadrature Hybrid for Multiphase Signals Generation. Chen, H.-S., +, TMTT Jan. 2012 131-138 An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer. Pohl, N., +, TMTT March 2012 757-765 Analysis of a New 33–58-GHz Doubly Balanced Drain Mixer in 90-nm CMOS Technology. Yang, H.-Y., +, TMTT April 2012 1057-1068 Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin. Ziegler, V., +, TMTT Dec. 2012 4209-4219 Design of 40–108-GHz Low-Power and High-Speed CMOS Up-/DownConversion Ring Mixers for Multistandard MMW Radio Applications. Tsai, J.-H., +, TMTT March 2012 670-678 Resistive Graphene FET Subharmonic Mixers: Noise and Linearity Assessment. Andersson, M. A., +, TMTT Dec. 2012 4035-4042 Mixing Distributed Modeling of Six-Port Transformer for Millimeter-Wave SiGe BiCMOS Circuits Design. Hou, D., +, TMTT Dec. 2012 3728-3738 On the Equivalence Between the Maxwell-Garnett Mixing Rule and the Debye Relaxation Formula. Salski, B., +, TMTT Aug. 2012 2352-2358 MMIC A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490 A Fully Integrated 0.18- m CMOS Transceiver Chip for -Band PhasedArray Systems. Gharibdoust, K., +, TMTT July 2012 2192-2202 A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 Design and Analysis of a Tri-Band Dual-Mode Chip Filter for 60-, 77-, and 100-GHz Applications. Yang, C.-L., +, TMTT April 2012 989-997 Security Pre-screening of Moving Persons Using a Rotating Multichannel -Band Radar. Hantscher, S., +, TMTT March 2012 870-880 Subharmonic 220- and 320-GHz SiGe HBT Receiver Front-Ends. Ojefors, E., +, TMTT May 2012 1397-1404 MMIC amplifiers 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 A Dual-Band 10/24-GHz Amplifier Design Incorporating Dual-Frequency Complex Load Matching. Hsieh, K.-A., +, TMTT June 2012 1649-1657 Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 MMIC frequency converters Design and Analysis of an Ultra-Wideband Automatic Self-Calibrating Upconverter in 65-nm CMOS. Kang, B., +, TMTT July 2012 2178-2191

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MMIC mixers Design and Analysis of Down-Conversion Gate/Base-Pumped Harmonic Mixers Using Novel Reduced-Size 180 Hybrid With Different Input Frequencies. Kuo, J.-J., +, TMTT Aug. 2012 2473-2485 Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 MMIC oscillators A Dual-Resonant Mode 10/22-GHz VCO With a Novel Inductive Switching Approach. Liu, S.-L., +, TMTT July 2012 2165-2177 A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 MMIC phase shifters 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 MMIC power amplifiers 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules. Florian, C., +, TMTT June 2012 1805-1816 Analysis and Design of a Stacked Power Amplifier With Very High Bandwidth. Fritsche, D., +, TMTT Oct. 2012 3223-3231 Novel MMIC Power Amplifier Linearization Utilizing Input Reflected Nonlinearity. Kuo, N.-C., +, TMTT March 2012 542-554 Power Amplification at 0.65 THz Using InP HEMTs. Radisic, V., +, TMTT March 2012 724-729 MMICs 4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers. Aja Abelan, B., +, TMTT Dec. 2012 4080-4088 Corrections to "An ultra-broad-band reflection-type phase-shifter MMIC with series and parallel LC circuits" [Dec 01 2446-2452]. Honari, M. M., +, TMTT Nov. 2012 3633 Mobile antennas A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module. Suga, R., +, TMTT March 2012 640-646 Mobile handsets A Multiband Reconfigurable Power Amplifier for UMTS Handset Applications. Kim, U., +, TMTT Aug. 2012 2532-2542 Ear Temperature Increase Produced by Cellular Phones Under Extreme Exposure Conditions. De Santis, V., +, TMTT June 2012 1728-1734 Mechanisms of RF Electromagnetic Field Absorption in Human Hands and Fingers. Li, C.-H., +, TMTT July 2012 2267-2276 Mobile radio Autoregressive Modeling of Mobile Radio Propagation Channel in Building Ruins. Chen, L., +, TMTT May 2012 1478-1489 Mode matching A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 Efficient Analysis of Metallic and Dielectric Posts in Parallel-Plate Waveguide Structures. Casaletti, M., +, TMTT Oct. 2012 2979-2989 Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network. Penaranda-Foix, F. L., +, TMTT Sept. 2012 2730-2740 Modulation Analysis and Implementation of Doherty Power Amplifier With Two-Point Envelope Modulation. Kim, J. H., +, TMTT May 2012 1353-1364 Digital Predistortion for High Efficiency Power Amplifier Architectures Using a Dual-Input Modeling Approach. Cao, H., +, TMTT Feb. 2012 361-369 Modulators 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 A Single Envelope Modulator-Based Envelope-Tracking Structure for Multiple-Input and Multiple-Output Wireless Transmitters. Yu, C., +, TMTT Oct. 2012 3317-3327 Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators. Gupta, A. K., +, TMTT Oct. 2012 3272-3285 The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration. Diehl, J. F., +, TMTT Jan. 2012 195-200 Monolithic integrated circuits A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299

+ Check author entry for coauthors

Monopole antennas A Fully SiP Integrated -Band Butler Matrix End-Fire Beam-Switching Transmitter Using Flip-Chip Assembled CMOS Chips on LTCC. Kuo, C.-C., +, TMTT May 2012 1424-1436 Monte Carlo methods Terahertz Micromachined On-Wafer Probes: Repeatability and Reliability. Chen, L., +, TMTT Sept. 2012 2894-2902 Variability Analysis of Multiport Systems Via Polynomial-Chaos Expansion. Spina, D., +, TMTT Aug. 2012 2329-2338 MOS analogue integrated circuits A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490 MOSFETs A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 CMOS Integrated Antenna-Coupled Field-Effect Transistors for the Detection of Radiation From 0.2 to 4.3 THz. Boppel, S., +, TMTT Dec. 2012 3834-3843 Design-in-Reliable Millimeter-Wave Power Amplifiers in a 65-nm CMOS Process. Quemerais, T., +, TMTT April 2012 1079-1085 LDMOS Technology for RF Power Amplifiers. Theeuwen, S. J. C. H., +, TMTT June 2012 1755-1763 Localized Rapid Heating by Low-Power Solid-State Microwave Drill. Meir, Y., +, TMTT Aug. 2012 2665-2672 in the Modeling Inductive Behavior of MOSFET Scattering Parameter Breakdown Regime. Lee, C.-I., +, TMTT March 2012 502-508 Multiaccess communication High-Gain and High-Efficiency EER/Polar Transmitters Using InjectionLocked Oscillators. Chen, C.-T., +, TMTT Dec. 2012 4117-4128 Multichip modules 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 Multiconductor transmission lines Generalized Time-Domain Adjoint Sensitivity Analysis of Distributed MTL Networks. Saini, A. S., +, TMTT Nov. 2012 3359-3368 Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 Multiplexing Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines. Sun, J. S., +, TMTT Dec. 2012 3950-3958 Multiport networks Robust Analog Canceller for High-Dynamic-Range Radio Frequency Measurement. Wetherington, J. M., +, TMTT June 2012 1709-1719 Robust Passive Macro-Model Generation With Local Compensation. Wang, T., +, TMTT Aug. 2012 2313-2328 Mutual coupling Distributed Modeling of Six-Port Transformer for Millimeter-Wave SiGe BiCMOS Circuits Design. Hou, D., +, TMTT Dec. 2012 3728-3738

N Nanobioscience Accurate Nanoliter Liquid Characterization Up to 40 GHz for Biomedical Applications: Toward Noninvasive Living Cells Monitoring. Chen, T., +, TMTT Dec. 2012 4171-4177 Nanotechnology ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process. Lin, C.-Y., +, TMTT March 2012 714-723 Nanowires Self-Biased Nonreciprocal Microstrip Phase Shifter on Magnetic Nanowired Substrate Suitable for Gyrator Applications. Hamoir, G., +, TMTT July 2012 2152-2157 Narrowband Widely Tunable High-Efficiency Power Amplifier With Ultra-Narrow Instantaneous Bandwidth. Chen, K., +, TMTT Dec. 2012 3787-3797 Nematic liquid crystals A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Network analyzers 16-Term Error Model in Reciprocal Systems. Silvonen, K., +, TMTT Nov. 2012 3551-3558 A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 An Analytical Formulation for Black Box Conversion Matrix Extraction. Kheirdoost, A., +, TMTT June 2012 1493-1499 Authors’ reply. Chen, G., +, TMTT June 2012 1745-1747 Device Characterization Techniques Based on Causal Relationships. Wojnowski, M., +, TMTT July 2012 2203-2219 Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide. Zhang, L., +, TMTT Jan. 2012 1-7 Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 New Trends for the Nonlinear Measurement and Modeling of High-Power RF Transistors and Amplifiers With Memory Effects. Roblin, P., +, TMTT June 2012 1964-1978 Passive Wireless Temperature Sensor Based on Time-Coded UWB Chipless RFID Tags. Girbau, D., +, TMTT Nov. 2012 3623-3632 Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses. Arnedo, I., +, TMTT May 2012 1244-1257 Network synthesis A Highly Linear and Efficient CMOS RF Power Amplifier With a 2-D Circuit Synthesis Technique. Ding, M., +, TMTT Sept. 2012 2851-2862 Comments on “Theoretical and Experimental Study of a New Class of Reflectionless Filter”. Roy, S. C. D., +, TMTT March 2012 632-633 Design and Analysis of a Tri-Band Dual-Mode Chip Filter for 60-, 77-, and 100-GHz Applications. Yang, C.-L., +, TMTT April 2012 989-997 Design of a New Type Planar Balun by Using Trans-Directional Couplers. Shie, C.-I., +, TMTT March 2012 471-476 Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology. Qian, S., +, TMTT Sept. 2012 2799-2807 Network topology -Band CMOS Differential and Quadrature Voltage-Controlled Oscillators for Low Phase-Noise and Low-Power Applications. Chang, H.-Y., +, TMTT Jan. 2012 46-59 A CMOS Distributed Amplifier With Distributed Active Input Balun Using GBW and Linearity Enhancing Techniques. Jahanian, A., +, TMTT May 2012 1331-1341 Analysis of a New 33–58-GHz Doubly Balanced Drain Mixer in 90-nm CMOS Technology. Yang, H.-Y., +, TMTT April 2012 1057-1068 Compact Wideband Linear CMOS Variable Gain Amplifier for Analog-Predistortion Power Amplifiers. Huang, Y.-Y., +, TMTT Jan. 2012 68-76 Low-Voltage, Wide-Locking-Range, Millimeter-Wave Divide-by-5 Injection-Locked Frequency Dividers. Li, M.-W., +, TMTT March 2012 679-685 Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828 Narrowband Microwave Filters With Mixed Topology. Macchiarella, G., +, TMTT Dec. 2012 3980-3987 Neural networks Complex-Chebyshev Functional Link Neural Network Behavioral Model for Broadband Wireless Power Amplifiers. Li, M., +, TMTT June 2012 1979-1989 Noise measurement A Unified Theory for -Parameter Uncertainty Evaluation. Garelli, M., +, TMTT Dec. 2012 3844-3855 An 8-bit Integrate-and-Sample Receiver for Rate-Scalable Photonic Analog-to-Digital Conversion. Gathman, T. D., +, TMTT Dec. 2012 3798-3809 Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique. Yeh, H.-C., +, TMTT Dec. 2012 4066-4079 Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique. Yeh, H.-C., +, TMTT Dec. 2012 4066-4079 Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467 Resistive Graphene FET Subharmonic Mixers: Noise and Linearity Assessment. Andersson, M. A., +, TMTT Dec. 2012 4035-4042

+ Check author entry for coauthors

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Noise shaping 4–12- and 25–34-GHz Cryogenic mHEMT MMIC Low-Noise Amplifiers. Aja Abelan, B., +, TMTT Dec. 2012 4080-4088 Nondestructive testing Performance Limitations and Measurement Analysis of a Near-Field Microwave Microscope for Nondestructive and Subsurface Detection. Chisum, J. D., +, TMTT Aug. 2012 2605-2615 Nonlinear distortion Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers. Yu, C., +, TMTT Dec. 2012 4198-4208 Notch filters A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 Extended Passband Bandstop Filter Cascade With Continuous 0.85–6.6-GHz Coverage. Naglich, E. J., +, TMTT Jan. 2012 21-30 Intrinsically Switched Varactor-Tuned Filters and Filter Banks. Guyette, A. C., +, TMTT April 2012 1044-1056 Miniaturized UWB Filters Integrated With Tunable Notch Filters Using a Silicon-Based Integrated Passive Device Technology. Wu, Z., +, TMTT March 2012 518-527 Numerical analysis A Generalized Multiple Scattering Method for Dense Vias With Axially Anisotropic Modes in an Arbitrarily Shaped Plate Pair. Zhang, Y.-J., +, TMTT July 2012 2035-2045 Even- and Odd-Mode Analysis of Thick and Wide Transverse Slot in Waveguides Based on a Variational Method. Wenzhi, W., +, TMTT Nov. 2012 3349-3358 Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 Generalized Time-Domain Adjoint Sensitivity Analysis of Distributed MTL Networks. Saini, A. S., +, TMTT Nov. 2012 3359-3368 Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide. Zhang, L., +, TMTT Jan. 2012 1-7 Numerical stability Numerical Stability and Dispersion Analysis of the Precise-Integration Time-Domain Method in Lossy Media. Sun, G., +, TMTT Sept. 2012 2723-2729 O Object detection Security Pre-screening of Moving Persons Using a Rotating Multichannel -Band Radar. Hantscher, S., +, TMTT March 2012 870-880 OFDM modulation Peak-Power Controlled Digital Predistorters for RF Power Amplifiers. Landin, P. N., +, TMTT Nov. 2012 3582-3590 Peak-Power Controlling Technique for Enhancing Digital Pre-Distortion of RF Power Amplifiers. Nader, C., +, TMTT Nov. 2012 3571-3581 Performance Enhancement of an OFDM Ultra-Wideband Transmission-Over-Fiber Link Using a Linearized Mixed-Polarization Single-Drive X-Cut Mach–Zehnder Modulator. Hraimel, B., +, TMTT Oct. 2012 3328-3338 Operational amplifiers A Precise Decibel-Linear Programmable Gain Amplifier Using a Constant Current-Density Function. Kang, S.-Y., +, TMTT Sept. 2012 2843-2850 Design of 40–108-GHz Low-Power and High-Speed CMOS Up-/DownConversion Ring Mixers for Multistandard MMW Radio Applications. Tsai, J.-H., +, TMTT March 2012 670-678 Optical arrays Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Optical communication equipment Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Optical distortion An 8-bit Integrate-and-Sample Receiver for Rate-Scalable Photonic Analog-to-Digital Conversion. Gathman, T. D., +, TMTT Dec. 2012 3798-3809

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Optical fabrication Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Optical fibers Exact and Closed-Form Cutoff Wavenumbers of Elliptical Dielectric Waveguides. Zouros, G. P., +, TMTT Sept. 2012 2741-2751 Optical filters A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM. Zong, Z.-Y., +, TMTT June 2012 1500-1512 Optical links Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links. Alcaro, G., +, TMTT Jan. 2012 185-194 The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration. Diehl, J. F., +, TMTT Jan. 2012 195-200 Optical modulation A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 Optical Modulation of Millimeter-Wave Beams Using a Semiconductor Substrate. Gallacher, T. F., +, TMTT July 2012 2301-2309 Optical multilayers Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Optical planar waveguides Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Optical projectors Optical Modulation of Millimeter-Wave Beams Using a Semiconductor Substrate. Gallacher, T. F., +, TMTT July 2012 2301-2309 Optical pulses An 8-bit Integrate-and-Sample Receiver for Rate-Scalable Photonic Analog-to-Digital Conversion. Gathman, T. D., +, TMTT Dec. 2012 3798-3809 Optical receivers A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 An 8-bit Integrate-and-Sample Receiver for Rate-Scalable Photonic Analog-to-Digital Conversion. Gathman, T. D., +, TMTT Dec. 2012 3798-3809 Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links. Alcaro, G., +, TMTT Jan. 2012 185-194 Optical switches Efficient Low-Frequency Breakdown Free Full-Wave PEEC Modeling Based on Geometrical Optics DCIM. Zong, Z.-Y., +, TMTT June 2012 1500-1512 Optical transceivers Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks. Cantu, H. I., +, TMTT Sept. 2012 2903-2912 Optical transmitters A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links. Alcaro, G., +, TMTT Jan. 2012 185-194 Optical tuning A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 Optical waveguide theory Exact and Closed-Form Cutoff Wavenumbers of Elliptical Dielectric Waveguides. Zouros, G. P., +, TMTT Sept. 2012 2741-2751 Optical waveguides A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide. Lee, J.-W., +, TMTT Dec. 2012 3642-3655 + Check author entry for coauthors

Optimization Broadband 90 Differential Phase Shifter Constructed Using a Pair of Multisection Radial Line Stubs. Yeung, S. H., +, TMTT Sept. 2012 2760-2767 Design of CMOS Power Amplifiers. Niknejad, A. M., +, TMTT June 2012 1784-1796 Microwave Chemical Sensing at Room Temperature Using an Overmoded Waveguide Design. Huang, Y.-T., +, TMTT Sept. 2012 2886-2893 Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology. Qian, S., +, TMTT Sept. 2012 2799-2807 Oscillations A -Band Capacitor-Coupled QVCO Using Sinusoidal Current Bias Technique. Shen, I.-S., +, TMTT Feb. 2012 318-328 Oscillators 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer. Tang, A., +, TMTT Dec. 2012 4129-4137 A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications. Kim, S., +, TMTT Dec. 2012 4178-4186 Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Experimental Characterization of Stability Margins in Microwave Amplifiers. Otegi, N., +, TMTT Dec. 2012 4145-4156 High-Gain and High-Efficiency EER/Polar Transmitters Using InjectionLocked Oscillators. Chen, C.-T., +, TMTT Dec. 2012 4117-4128 Large-Signal Oscillator Design Procedure Utilizing Analytical -Parameters Closed-Form Expressions. Pelaez-Perez, A. M., +, TMTT Oct. 2012 3126-3136 Low-Power Sub-Harmonic Direct-Conversion Receiver With Tunable RF LNA and Wideband LO Generator at U-NII Bands. Syu, J.-S., +, TMTT March 2012 555-566 Passive Subharmonic Generation Using Memoryless Nonlinear Circuits. Safarian, Z., +, TMTT Dec. 2012 4053-4065 Subharmonic 220- and 320-GHz SiGe HBT Receiver Front-Ends. Ojefors, E., +, TMTT May 2012 1397-1404

P P-i-n diodes Microwave and RF p-i-n Diode Model for Time-Domain Simulation. Caverly, R. H., +, TMTT July 2012 2158-2164 Variable Reflection-Type Attenuators Based on Varactor Diodes. Bulja, S., +, TMTT Dec. 2012 3719-3727 Packaging Millimeter-Wave Technology for Automotive Radar Sensors in the 77 GHz Frequency Band. Hasch, J., +, TMTT March 2012 845-860 Packet radio networks Single-Chip Multiband EGPRS and SAW-Less LTE WCDMA CMOS Receiver With Diversity. Xie, H., +, TMTT May 2012 1390-1396 Parallel architectures MPIE/MoM Acceleration With a General-Purpose Graphics Processing Unit. De Donno, D., +, TMTT Sept. 2012 2693-2701 Parallel plate waveguides Characterization of Waveguides With a Combination of Conductor and Periodic Boundary Contours: Application to the Analysis of Bi-Periodic Structures. Varela, J. E., +, TMTT March 2012 419-430 Efficient Analysis of Metallic and Dielectric Posts in Parallel-Plate Waveguide Structures. Casaletti, M., +, TMTT Oct. 2012 2979-2989 Parameter estimation Optimized Low-Complexity Implementation of Least Squares Based Model Extraction for Digital Predistortion of RF Power Amplifiers. Guan, L., +, TMTT March 2012 594-603 Passband Wideband Dual-Mode Microstrip Filter Using Short-Ended Resonator With Centrally Loaded Inductive Stub. Sun, S.-J., +, TMTT Dec. 2012 3667-3673

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Passive networks A 1.2-V 5.2-mW 20–30-GHz Wideband Receiver Front-End in 0.18- m CMOS. Li, C.-H., +, TMTT Nov. 2012 3502-3512 Analysis of a New 33–58-GHz Doubly Balanced Drain Mixer in 90-nm CMOS Technology. Yang, H.-Y., +, TMTT April 2012 1057-1068 Passivity Enforcement for Admittance Models of Distributed Networks Using an Inverse Eigenvalue Method. Saunders, C. S., +, TMTT Jan. 2012 8-20 Portable Space Mapping for Efficient Statistical Modeling of Passive Components. Zhang, L., +, TMTT March 2012 441-450 Robust Passive Macro-Model Generation With Local Compensation. Wang, T., +, TMTT Aug. 2012 2313-2328 Patch antennas On the Detection of Frequency-Spectra-Based Chipless RFID Using UWB Impulsed Interrogation. Kalansuriya, P., +, TMTT Dec. 2012 4187-4197 Periodic structures Characterization of Waveguides With a Combination of Conductor and Periodic Boundary Contours: Application to the Analysis of Bi-Periodic Structures. Varela, J. E., +, TMTT March 2012 419-430 Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides. Ochoa, J. S., +, TMTT Dec. 2012 3919-3926 Nonperiodic Perturbations in Periodic RF Structures. Jabotinski, V., +, TMTT April 2012 915-929 Simulation and Measurement of the -Parameters of Obstacles in Periodic Waveguides. Navarro-Tapia, M., +, TMTT April 2012 1146-1155 Permeability Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies. Bayatpur, F., +, TMTT April 2012 1126-1135 Self-Biased Nonreciprocal Microstrip Phase Shifter on Magnetic Nanowired Substrate Suitable for Gyrator Applications. Hamoir, G., +, TMTT July 2012 2152-2157 Permittivity A 1–8-GHz Miniaturized Spectroscopy System for Permittivity Detection and Mixture Characterization of Organic Chemicals. Helmy, A. A., +, TMTT Dec. 2012 4157-4170 A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals. Polycarpou, A. C., +, TMTT Oct. 2012 2950-2958 A Self-Sustained Microwave System for Dielectric-Constant Measurement of Lossy Organic Liquids. Sekar, V., +, TMTT May 2012 1444-1455 Buried Object Characterization Using Ultra-Wideband Ground Penetrating Radar. Li, L., +, TMTT Aug. 2012 2654-2664 Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies. Bayatpur, F., +, TMTT April 2012 1126-1135 Multilayer Antenna-Filter Antenna for Beam-Steering Transmit-Array Applications. Boccia, L., +, TMTT July 2012 2287-2300 Numerical Stability and Dispersion Analysis of the Precise-Integration Time-Domain Method in Lossy Media. Sun, G., +, TMTT Sept. 2012 2723-2729 Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation. Kilic, E., +, TMTT May 2012 14371443 Permittivity measurement Novel Coupling Structure for the Resonant Coaxial Probe. Rowe, D. J., +, TMTT June 2012 1699-1708 Personal area networks A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module. Suga, R., +, TMTT March 2012 640-646 Perturbation techniques Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide. Zhang, L., +, TMTT Jan. 2012 1-7 Phantoms Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 Frequency Multiplexed 2-Dimensional Sensor Array Based on Split-Ring Resonators for Organic Tissue Analysis. Puentes, M., +, TMTT June 2012 1720-1727 Mechanisms of RF Electromagnetic Field Absorption in Human Hands and Fingers. Li, C.-H., +, TMTT July 2012 2267-2276 New Method for Determining Dielectric Properties of Skin and Phantoms at Millimeter Waves Based on Heating Kinetics. Chahat, N., +, TMTT March 2012 827-832 Phase control 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 + Check author entry for coauthors

4279

A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications. Son, K. Y., +, TMTT Aug. 2012 2571-2580 Phase detectors A Waveform-Dependent Phase-Noise Analysis for Edge-Combining DLL Frequency Multipliers. Liao, F.-R., +, TMTT April 2012 1086-1096 Phase locked loops A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A 64–84-GHz PLL With Low Phase Noise in an 80-GHz SiGe HBT Technology. Liu, G., +, TMTT Dec. 2012 3739-3748 A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer. Pohl, N., +, TMTT March 2012 757-765 Design and Analysis of a -band Divide-by-Three Injection-Locked Frequency Divider Using Second Harmonic Enhancement Technique. Yeh, Y.-L., +, TMTT June 2012 1617-1625 Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Phase locked oscillators Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks. Cantu, H. I., +, TMTT Sept. 2012 2903-2912 Phase modulation A 50-Mb/s CMOS QPSK/O-QPSK Transmitter Employing Injection Locking for Direct Modulation. Diao, S., +, TMTT Jan. 2012 120-130 A Narrow-Passband and Frequency-Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT May 2012 1287-1296 A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 High-Gain and High-Efficiency EER/Polar Transmitters Using InjectionLocked Oscillators. Chen, C.-T., +, TMTT Dec. 2012 4117-4128 Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator. Mortazy, E., +, TMTT Feb. 2012 293-300 Phase noise -Band CMOS Differential and Quadrature Voltage-Controlled Oscillators for Low Phase-Noise and Low-Power Applications. Chang, H.-Y., +, TMTT Jan. 2012 46-59 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission. Hirata, A., +, TMTT March 2012 881-895 A -Band Capacitor-Coupled QVCO Using Sinusoidal Current Bias Technique. Shen, I.-S., +, TMTT Feb. 2012 318-328 A 64–84-GHz PLL With Low Phase Noise in an 80-GHz SiGe HBT Technology. Liu, G., +, TMTT Dec. 2012 3739-3748 A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 A Waveform-Dependent Phase-Noise Analysis for Edge-Combining DLL Frequency Multipliers. Liao, F.-R., +, TMTT April 2012 1086-1096 A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating. Li, W., +, TMTT June 2012 1735-1742 Analysis and Design of Low Phase-Noise Oscillators With Nonlinear Resonators. Imani, A., +, TMTT Dec. 2012 3749-3760 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation. Jooyaie, A., +, TMTT Aug. 2012 2505-2511 Pulse-Biased Low-Power Low-Phase-Noise UHF LC-QVCO for 866 MHz RFID Front-End. Li, J., +, TMTT Oct. 2012 3120-3125 Phase shift keying Design of 40–108-GHz Low-Power and High-Speed CMOS Up-/DownConversion Ring Mixers for Multistandard MMW Radio Applications. Tsai, J.-H., +, TMTT March 2012 670-678

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Phase shifters 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 A 44–46-GHz 16-Element SiGe BiCMOS High-Linearity Transmit/Receive Phased Array. Kim, C.-Y., +, TMTT March 2012 730-742 A Phased Array RFIC With Built-In Self-Test Capabilities. Inac, O., +, TMTT Jan. 2012 139-148 An Ultra-Compact, Linearly-Controlled Variable Phase Shifter Designed With a Novel RC Poly-Phase Filter. Huang, Y.-Y., +, TMTT Feb. 2012 301-310 Broadband 90 Differential Phase Shifter Constructed Using a Pair of Multisection Radial Line Stubs. Yeung, S. H., +, TMTT Sept. 2012 2760-2767 Comments on "Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter". Sun, Z., +, TMTT Sept. 2012 2934 Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter. Lin, F., +, TMTT May 2012 1226-1234 Corrections to "An ultra-broad-band reflection-type phase-shifter MMIC with series and parallel LC circuits" [Dec 01 2446-2452]. Honari, M. M., +, TMTT Nov. 2012 3633 Self-Biased Nonreciprocal Microstrip Phase Shifter on Magnetic Nanowired Substrate Suitable for Gyrator Applications. Hamoir, G., +, TMTT July 2012 2152-2157 Simulation and Experiment of a Compact Wideband 90 Differential Phase Shifter. Sorn, M., +, TMTT March 2012 494-501 Photoconductivity The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration. Diehl, J. F., +, TMTT Jan. 2012 195-200 Photodiodes 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission. Hirata, A., +, TMTT March 2012 881-895 Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes. Rouvalis, E., +, TMTT March 2012 509-517 Millimeter-Wave Optoelectronic Mixers Based on Uni-Traveling Carrier Photodiodes. Rouvalis, E., +, TMTT March 2012 686-691 The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration. Diehl, J. F., +, TMTT Jan. 2012 195-200 Photoemission The Performance of a Fiber-Optic Link Using Unbiased Balanced Photodiodes for Antenna Array Calibration. Diehl, J. F., +, TMTT Jan. 2012 195-200 Photonics An 8-bit Integrate-and-Sample Receiver for Rate-Scalable Photonic Analog-to-Digital Conversion. Gathman, T. D., +, TMTT Dec. 2012 3798-3809 Photoresists Vertical RF Transition With Mechanical Fit for 3-D Heterogeneous Integration. Chen, L., +, TMTT March 2012 647-654 Photovoltaic cells An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications. Kim, S., +, TMTT Dec. 2012 4178-4186 Piezoelectric transducers Compact, Low-Loss, Wideband, and High-Power Handling Phase Shifters With Piezoelectric Transducer-Controlled Metallic Perturber. Wu, J., +, TMTT June 2012 1587-1594 Planar antennas A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 Platinum alloys An All-Metal Micro-Relay With Bulk Foil Pt–Rh Contacts for High-Power RF Applications. Ozkeskin, F. M., +, TMTT June 2012 1595-1604 Pneumodynamics Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Polarization A Novel Compact Printable Dual-Polarized Chipless RFID System. Islam, M. A., +, TMTT July 2012 2142-2151

+ Check author entry for coauthors

Polarization-Independent Metamaterial Analog of Electromagnetically Induced Transparency for a Refractive-Index-Based Sensor. Meng, F.-Y., +, TMTT Oct. 2012 3013-3022 Poles and zeros Analysis of Composite Right/Left-Handed Unit Cells Based on Even–OddMode Excitation. Eberspacher, M. A., +, TMTT May 2012 1186-1196 Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators. Ahn, H.-R., +, TMTT June 2012 1549-1559 Narrowband Microwave Filters With Mixed Topology. Macchiarella, G., +, TMTT Dec. 2012 3980-3987 Novel Wideband Differential Bandpass Filters Based on T-Shaped Structure. Feng, W., +, TMTT June 2012 1560-1568 Polymers Broadband CMOS Millimeter-Wave Frequency Multiplier With Vivaldi Antenna in 3-D Chip-Scale Packaging. Tripodi, L., +, TMTT Dec. 2012 37613768 Polynomials A New High-Efficient Spectral-Domain Analysis of Single and Multiple Coupled Microstrip Lines in Planarly Layered Media. Lucido, M., +, TMTT July 2012 2025-2034 Graphical Analysis of Stabilization Loss and Gains for Three-Port Networks. Tan, E. L., +, TMTT June 2012 1635-1640 Narrowband Microwave Filters With Mixed Topology. Macchiarella, G., +, TMTT Dec. 2012 3980-3987 Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay. Zhang, Q., +, TMTT Aug. 2012 2394-2402 Variability Analysis of Multiport Systems Via Polynomial-Chaos Expansion. Spina, D., +, TMTT Aug. 2012 2329-2338 Power amplifiers 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A Broadband Injection-Locking Class-E Power Amplifier. Lin, C.-H., +, TMTT Oct. 2012 3232-3242 A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications. Son, K. Y., +, TMTT Aug. 2012 2571-2580 A Dual-Band Parallel Doherty Power Amplifier for Wireless Applications. Grebennikov, A., +, TMTT Oct. 2012 3214-3222 A Dual-Mode CMOS RF Power Amplifier With Integrated Tunable Matching Network. Yoon, Y., +, TMTT Jan. 2012 77-88 A Fully Integrated Adaptive Multiband Multimode Switching-Mode CMOS Power Amplifier. Aref, A. F., +, TMTT Aug. 2012 2549-2561 A High-Efficiency Low-Distortion GaN HEMT Doherty Power Amplifier With a Series-Connected Load. Kawai, S., +, TMTT Feb. 2012 352-360 A Highly Linear and Efficient CMOS RF Power Amplifier With a 2-D Circuit Synthesis Technique. Ding, M., +, TMTT Sept. 2012 2851-2862 A Multiband Reconfigurable Power Amplifier for UMTS Handset Applications. Kim, U., +, TMTT Aug. 2012 2532-2542 A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 A Single Envelope Modulator-Based Envelope-Tracking Structure for Multiple-Input and Multiple-Output Wireless Transmitters. Yu, C., +, TMTT Oct. 2012 3317-3327 A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications. Hassan, M., +, TMTT May 2012 1321-1330 A Zero-Voltage-Switching Contour-Based Outphasing Power Amplifier. Singhal, N., +, TMTT June 2012 1896-1906 An Ultra-Compact, Linearly-Controlled Variable Phase Shifter Designed With a Novel RC Poly-Phase Filter. Huang, Y.-Y., +, TMTT Feb. 2012 301-310 Analysis and Implementation of Doherty Power Amplifier With Two-Point Envelope Modulation. Kim, J. H., +, TMTT May 2012 1353-1364 Analytical Design Methodology of Outphasing Amplification Systems Using a New Simplified Chireix Combiner Model. El-Asmar, M., +, TMTT June 2012 1886-1895 Behaviors of Class-F and Class-F Amplifiers. Moon, J., +, TMTT June 2012 1937-1951 Broadband Doherty Power Amplifier via Real Frequency Technique. Sun, G., +, TMTT Jan. 2012 99-111

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Closed-Loop Digital Predistortion System With Fast Real-Time Adaptation Applied to a Handset WCDMA PA Module. Presti, C. D., +, TMTT March 2012 604-618 Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters. Hoversten, J., +, TMTT June 2012 2010-2020 Compact Wideband Linear CMOS Variable Gain Amplifier for Analog-Predistortion Power Amplifiers. Huang, Y.-Y., +, TMTT Jan. 2012 68-76 Complex-Chebyshev Functional Link Neural Network Behavioral Model for Broadband Wireless Power Amplifiers. Li, M., +, TMTT June 2012 1979-1989 Controlling Active Load–Pull in a Dual-Input Inverse Load Modulated Doherty Architecture. Hone, T. M., +, TMTT June 2012 1797-1804 Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier. Saad, P., +, TMTT June 2012 1840-1849 Design of a Direct Conversion Transmitter to Resist Combined Effects of Power Amplifier Distortion and Local Oscillator Pulling. Hsiao, C.-H., +, TMTT June 2012 2000-2009 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier Using In-Band Continuous Class-F F Mode Transferring. Chen, K., +, TMTT Dec. 2012 4107-4116 Design of CMOS Power Amplifiers. Niknejad, A. M., +, TMTT June 2012 1784-1796 Design-in-Reliable Millimeter-Wave Power Amplifiers in a 65-nm CMOS Process. Quemerais, T., +, TMTT April 2012 1079-1085 Digital Predistortion for High Efficiency Power Amplifier Architectures Using a Dual-Input Modeling Approach. Cao, H., +, TMTT Feb. 2012 361-369 Guest Editorial. Popovic, Z., +, TMTT June 2012 1753-1754 High-Efficiency Cellular Power Amplifiers Based on a Modified LDMOS Process on Bulk Silicon and Silicon-On-Insulator Substrates With Integrated Power Management Circuitry. Tombak, A., +, TMTT June 2012 1862-1869 Integrated Bias Circuits of RF CMOS Cascode Power Amplifier for Linearity Enhancement. Koo, B., +, TMTT Feb. 2012 340-351 Investigation of Wideband Load Transformation Networks for Class-E Switching-Mode Power Amplifiers. Wei, M.-D., +, TMTT June 2012 1916-1927 Modeling and Digital Predistortion of Class-D Outphasing RF Power Amplifiers. Landin, P. N., +, TMTT June 2012 1907-1915 Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828 New Trends for the Nonlinear Measurement and Modeling of High-Power RF Transistors and Amplifiers With Memory Effects. Roblin, P., +, TMTT June 2012 1964-1978 Optimized Load Modulation Network for Doherty Power Amplifier Performance Enhancement. Chen, S., +, TMTT Nov. 2012 3474-3481 Optimized Low-Complexity Implementation of Least Squares Based Model Extraction for Digital Predistortion of RF Power Amplifiers. Guan, L., +, TMTT March 2012 594-603 Parallel Frequency-Domain Simulation of Hyperspectral Waveforms in Nonlinear Power Amplifiers With Memory. Stantchev, G., +, TMTT April 2012 930-937 Peak-Power Controlling Technique for Enhancing Digital Pre-Distortion of RF Power Amplifiers. Nader, C., +, TMTT Nov. 2012 3571-3581 Ring-Resonator-Inspired Power Recycling Scheme for Gain-Enhanced Distributed Amplifier-Based CRLH-Transmission Line Leaky Wave Antennas. Wu, C.-T. M., +, TMTT April 2012 1027-1037 Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes. Suarez, A., +, TMTT March 2012 528-541 Subsampling Feedback Loop Applicable to Concurrent Dual-Band Linearization Architecture. Bassam, S. A., +, TMTT June 2012 1990-1999 The Continuous Inverse Class-F Mode With Resistive Second-Harmonic Impedance. Carrubba, V., +, TMTT June 2012 1928-1936 Theory and Design of Class-J Power Amplifiers With Dynamic Load Modulation. Andersson, C. M., +, TMTT Dec. 2012 3778-3786 Two-Way Current-Combining -Band Power Amplifier in 65-nm CMOS. Gu, Q. J., +, TMTT May 2012 1365-1374 Vectorially Combined Distributed Power Amplifiers for Software-Defined Radio Applications. Narendra, K., +, TMTT Oct. 2012 3189-3200

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Power combiners 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 A Fully Integrated Watt-Level Linear 900-MHz CMOS RF Power Amplifier for LTE-Applications. Francois, B., +, TMTT June 2012 1878-1885 A New Balanced-to-Balanced Power Divider/Combiner. Xia, B., +, TMTT Sept. 2012 2791-2798 All-Digital RF Modulator. Alavi, M. S., +, TMTT Nov. 2012 3513-3526 Analytical Design Methodology of Outphasing Amplification Systems Using a New Simplified Chireix Combiner Model. El-Asmar, M., +, TMTT June 2012 1886-1895 Design of a Broadband Eight-Way Coaxial Waveguide Power Combiner. Amjadi, M., +, TMTT Jan. 2012 39-45 Design of CMOS Power Amplifiers. Niknejad, A. M., +, TMTT June 2012 1784-1796 Microstrip Bandpass Filters With Various Resonators Using Connected- and Edge-Coupling Mechanisms and Their Applications to Dual-Band Filters and Diplexers. Lin, S.-C., +, TMTT April 2012 975-988 Power Amplification at 0.65 THz Using InP HEMTs. Radisic, V., +, TMTT March 2012 724-729 Two-Way Current-Combining -Band Power Amplifier in 65-nm CMOS. Gu, Q. J., +, TMTT May 2012 1365-1374 Power consumption A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications. Son, K. Y., +, TMTT Aug. 2012 2571-2580 Power control Peak-Power Controlled Digital Predistorters for RF Power Amplifiers. Landin, P. N., +, TMTT Nov. 2012 3582-3590 Peak-Power Controlling Technique for Enhancing Digital Pre-Distortion of RF Power Amplifiers. Nader, C., +, TMTT Nov. 2012 3571-3581 Power converters 60-GHz Dual-Conversion Down-/Up-Converters Using Schottky Diode in 0.18 m Foundry CMOS Technology. Wei, H.-J., +, TMTT June 2012 16841698 Power dividers 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 and A Generalized Dual-Band Wilkinson Power Divider With Parallel Components. Wang, X., +, TMTT April 2012 952-964 A Modified Wilkinson Power Divider With Isolation Bandwidth Improvement. Kao, J.-C., +, TMTT Sept. 2012 2768-2780 A New Balanced-to-Balanced Power Divider/Combiner. Xia, B., +, TMTT Sept. 2012 2791-2798 Authors’ reply. Lin, F., +, TMTT Sept. 2012 2935-2936 Comments on "Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter". Sun, Z., +, TMTT Sept. 2012 2934 Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter. Lin, F., +, TMTT May 2012 1226-1234 Design of Multiway Power Divider by Using Stepped-Impedance Transformers. Xu, Y., +, TMTT Sept. 2012 2781-2790 Novel Dual-Band Out-of-Phase Power Divider With High Power-Handling Capability. Dai, G.-L., +, TMTT Aug. 2012 2403-2409 Unequal Wilkinson Power Dividers With Favorable Selectivity and HighIsolation Using Coupled-Line Filter Transformers. Deng, P.-H., +, TMTT June 2012 1520-1529 Power generation A Modified Doherty Configuration for Broadband Amplification Using Symmetrical Devices. Wu, D. Y.-T., +, TMTT Oct. 2012 3201-3213 A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN. Chen, J.-H., +, TMTT Dec. 2012 4089-4096 PA Efficiency and Linearity Enhancement Using External Harmonic Injection. Dani, A., +, TMTT Dec. 2012 4097-4106 Theory and Design of Class-J Power Amplifiers With Dynamic Load Modulation. Andersson, C. M., +, TMTT Dec. 2012 3778-3786 Power supply circuits Digital Predistortion for High Efficiency Power Amplifier Architectures Using a Dual-Input Modeling Approach. Cao, H., +, TMTT Feb. 2012 361-369

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Power system harmonics PA Efficiency and Linearity Enhancement Using External Harmonic Injection. Dani, A., +, TMTT Dec. 2012 4097-4106 Power transistors A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 High-Efficiency Cellular Power Amplifiers Based on a Modified LDMOS Process on Bulk Silicon and Silicon-On-Insulator Substrates With Integrated Power Management Circuitry. Tombak, A., +, TMTT June 2012 1862-1869 New Trends for the Nonlinear Measurement and Modeling of High-Power RF Transistors and Amplifiers With Memory Effects. Roblin, P., +, TMTT June 2012 1964-1978 Power transmission lines A Modified Doherty Configuration for Broadband Amplification Using Symmetrical Devices. Wu, D. Y.-T., +, TMTT Oct. 2012 3201-3213 CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution. Gupta, S., +, TMTT Dec. 2012 3939-3949 Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines. Sun, J. S., +, TMTT Dec. 2012 3950-3958 Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity. Ruiz-Cruz, J. A., +, TMTT Dec. 2012 3969-3979 Predictive models Distributed Modeling of Six-Port Transformer for Millimeter-Wave SiGe BiCMOS Circuits Design. Hou, D., +, TMTT Dec. 2012 3728-3738 Predistortion Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers. Yu, C., +, TMTT Dec. 2012 4198-4208 Printed circuit design A High Slow-Wave Factor Microstrip Structure With Simple Design Formulas and Its Application to Microwave Circuit Design. Chang, W.-S., +, TMTT Nov. 2012 3376-3383 Printed circuit manufacture A High Slow-Wave Factor Microstrip Structure With Simple Design Formulas and Its Application to Microwave Circuit Design. Chang, W.-S., +, TMTT Nov. 2012 3376-3383 Printed circuits A Zero-Voltage-Switching Contour-Based Outphasing Power Amplifier. Singhal, N., +, TMTT June 2012 1896-1906 An All-Metal Micro-Relay With Bulk Foil Pt–Rh Contacts for High-Power RF Applications. Ozkeskin, F. M., +, TMTT June 2012 1595-1604 Conformal Ink-Jet Printed -Band Phased-Array Antenna Incorporating Carbon Nanotube Field-Effect Transistor Based Reconfigurable True-Time Delay Lines. Chen, M. Y., +, TMTT Jan. 2012 179-184 Millimeter-Wave Printed Circuit Board Characterization Using Substrate Integrated Waveguide Resonators. Zelenchuk, D. E., +, TMTT Oct. 2012 3300-3308 Substrate Integrated Waveguide Quasi-Elliptic Filters With Controllable Electric and Magnetic Mixed Coupling. Gong, K., +, TMTT Oct. 2012 3071-3078 Programmable circuits A High Dynamic-Range RF Programmable-Gain Front End for G.hn RF-Coax in 65-nm CMOS. Trulls, X., +, TMTT Oct. 2012 3243-3253 A Waveform-Dependent Phase-Noise Analysis for Edge-Combining DLL Frequency Multipliers. Liao, F.-R., +, TMTT April 2012 1086-1096 Prototypes Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines. Sun, J. S., +, TMTT Dec. 2012 3950-3958 Narrowband Microwave Filters With Mixed Topology. Macchiarella, G., +, TMTT Dec. 2012 3980-3987 PA Efficiency and Linearity Enhancement Using External Harmonic Injection. Dani, A., +, TMTT Dec. 2012 4097-4106 Pulse generators A Nonlinear Lattice for High-Amplitude Picosecond Pulse Generation in CMOS. Lee, W., +, TMTT Feb. 2012 370-380

+ Check author entry for coauthors

Q Q-factor A Dual-Resonant Mode 10/22-GHz VCO With a Novel Inductive Switching Approach. Liu, S.-L., +, TMTT July 2012 2165-2177 A Narrowband CMOS Ring Resonator Dual-Mode Active Bandpass Filter With Edge Periphery of 2% Free-Space Wavelength. Su, L., +, TMTT June 2012 1605-1616 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology. Kuylenstierna, D., +, TMTT Nov. 2012 3420-3430 Device Characterization Techniques Based on Causal Relationships. Wojnowski, M., +, TMTT July 2012 2203-2219 Independence of the Unloaded of a Planar Electromagnetic Resonator From Its Shape. Naji, A., +, TMTT Aug. 2012 2370-2377 Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Novel Second-Order Dual-Mode Dual-Band Filters Using Capacitance Loaded Square Loop Resonator. Fu, S., +, TMTT March 2012 477-483 Quadrature amplitude modulation A 30.8-dBm Wideband CMOS Power Amplifier With Minimized Supply Fluctuation. Jin, B., +, TMTT June 2012 1658-1666 A Broadband Injection-Locking Class-E Power Amplifier. Lin, C.-H., +, TMTT Oct. 2012 3232-3242 Modulator. Alavi, M. S., +, TMTT Nov. 2012 3513-3526 All-Digital RF Broadband Millimeter-Wave Single Balanced Mixer and Its Applications to Substrate Integrated Wireless Systems. Zhang, Z.-Y., +, TMTT March 2012 660-669 Design of a Direct Conversion Transmitter to Resist Combined Effects of Power Amplifier Distortion and Local Oscillator Pulling. Hsiao, C.-H., +, TMTT June 2012 2000-2009 Linearity Considerations for Low-EVM, Millimeter-Wave Direct-Conversion Modulators. Gupta, A. K., +, TMTT Oct. 2012 3272-3285 Novel Modeling and Calibration Approach for Multiport Receivers Mitigating System Imperfections and Hardware Impairments. Hasan, A., +, TMTT Aug. 2012 2644-2653 Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems. Thomas, S. J., +, TMTT April 2012 1175-1182 Quadrature phase shift keying 24-GHz Integrated Radio and Radar System Capable of Time-Agile Wireless Communication and Sensing. Han, L., +, TMTT March 2012 619-631 A 50-Mb/s CMOS QPSK/O-QPSK Transmitter Employing Injection Locking for Direct Modulation. Diao, S., +, TMTT Jan. 2012 120-130 Modulator. Alavi, M. S., +, TMTT Nov. 2012 3513-3526 All-Digital RF Multi-Gb/s Analog Synchronous QPSK Demodulator With Phase-Noise Suppression. Ulusoy, A. ., +, TMTT Nov. 2012 3591-3598 R Radar Analog Signal Processing for Pulse Compression Radar in 90-nm CMOS. Parlak, M., +, TMTT Dec. 2012 3810-3822 Radar antennas A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar. Jahn, M., +, TMTT March 2012 861-869 Analog Signal Processing for Pulse Compression Radar in 90-nm CMOS. Parlak, M., +, TMTT Dec. 2012 3810-3822 Radar cross-sections Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems. Thomas, S. J., +, TMTT April 2012 1175-1182 Radar detection Security Pre-screening of Moving Persons Using a Rotating Multichannel -Band Radar. Hantscher, S., +, TMTT March 2012 870-880 Radar imaging Buried Object Characterization Using Ultra-Wideband Ground Penetrating Radar. Li, L., +, TMTT Aug. 2012 2654-2664 Radar receivers An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794

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Design and Analysis of a 21–29-GHz Ultra-Wideband Receiver Front-End in 0.18- m CMOS Technology. Lin, Y.-S., +, TMTT Aug. 2012 2590-2604 Radar signal processing A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar. Jahn, M., +, TMTT March 2012 861-869 Radar transmitters A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator. Lee, S., +, TMTT May 2012 1405-1412 A 24-GHz CMOS UWB Radar Transmitter With Compressed Pulses. Yang, J., +, TMTT April 2012 1117-1125 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Radiation effects A Novel Model for Implementation of Gamma Radiation Effects in GaAs HBTs. Zhang, J., +, TMTT Dec. 2012 3693-3698 Radio applications Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Radio frequency An Ultra-Thin, High-Power, and Multilayer Organic Antenna Array With T/R Functionality in the -Band. Donado Morcillo, C. A., +, TMTT Dec. 2012 3856-3867 Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers. Yu, C., +, TMTT Dec. 2012 4198-4208 Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin. Ziegler, V., +, TMTT Dec. 2012 4209-4219 Guest Editorial. Rieh, J.-S., +, TMTT Dec. 2012 3641 Guest Editorial. Lin, F., +, TMTT Nov. 2012 3347-3348 High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers. Roberg, M., +, TMTT Dec. 2012 4043-4052 On the Compression and Blocking Distortion of Semiconductor-Based Varactors. Huang, C., +, TMTT Dec. 2012 3699-3709 Radio links 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission. Hirata, A., +, TMTT March 2012 881-895 Radio networks A Dual-Band Parallel Doherty Power Amplifier for Wireless Applications. Grebennikov, A., +, TMTT Oct. 2012 3214-3222 Radio receivers 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 A 130-nm CMOS 100-Hz–6-GHz Reconfigurable Vector Signal Analyzer and Software-Defined Receiver. Goel, A., +, TMTT May 2012 1375-1389 A Digital-Intensive Multimode Multiband Receiver Using a Sinc FilterEmbedded VCO-Based ADC. Kim, J., +, TMTT Oct. 2012 3254-3262 Low-Power Sub-Harmonic Direct-Conversion Receiver With Tunable RF LNA and Wideband LO Generator at U-NII Bands. Syu, J.-S., +, TMTT March 2012 555-566 Reconfigurable Dual-Channel Multiband RF Receiver for GPS/ Galileo/BD-2 Systems. Chen, D., +, TMTT Nov. 2012 3491-3501 Radio repeaters A Compact 3-D Harmonic Repeater for Passive Wireless Sensing. Nassar, I. T., +, TMTT Oct. 2012 3309-3316 Radio transceivers 24-GHz Integrated Radio and Radar System Capable of Time-Agile Wireless Communication and Sensing. Han, L., +, TMTT March 2012 619-631 A 1.1-V Regulator-Stabilized 21.4-GHz VCO and a 115% Frequency-Range Dynamic Divider for -Band Wireless Communication. Nakamura, T., +, TMTT Sept. 2012 2823-2832 A Fully Integrated 0.18- m CMOS Transceiver Chip for -Band PhasedArray Systems. Gharibdoust, K., +, TMTT July 2012 2192-2202 A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer. Pohl, N., +, TMTT March 2012 757-765 + Check author entry for coauthors

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Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks. Cantu, H. I., +, TMTT Sept. 2012 2903-2912 Radio transmitters 9-GHz Wideband CMOS RX and TX Front-Ends for Universal Radio Applications. Hampel, S. K., +, TMTT April 2012 1105-1116 A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters. Hoversten, J., +, TMTT June 2012 2010-2020 Design of a Direct Conversion Transmitter to Resist Combined Effects of Power Amplifier Distortion and Local Oscillator Pulling. Hsiao, C.-H., +, TMTT June 2012 2000-2009 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 Radio-over-fiber Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links. Alcaro, G., +, TMTT Jan. 2012 185-194 Performance Enhancement of an OFDM Ultra-Wideband Transmission-Over-Fiber Link Using a Linearized Mixed-Polarization Single-Drive X-Cut Mach–Zehnder Modulator. Hraimel, B., +, TMTT Oct. 2012 3328-3338 Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks. Cantu, H. I., +, TMTT Sept. 2012 2903-2912 Radiocommunication Diffraction in mm and Sub-mm Wave Indoor Propagation Channels. Jacob, M., +, TMTT March 2012 833-844 Mitigation of Bandwidth Limitation in Wireless Doherty Amplifiers With Substantial Bandwidth Enhancement Using Digital Techniques. Darraji, R., +, TMTT Sept. 2012 2875-2885 Radiofrequency amplifiers A Dual-Mode CMOS RF Power Amplifier With Integrated Tunable Matching Network. Yoon, Y., +, TMTT Jan. 2012 77-88 A High Dynamic-Range RF Programmable-Gain Front End for G.hn RF-Coax in 65-nm CMOS. Trulls, X., +, TMTT Oct. 2012 3243-3253 A Highly Linear and Efficient CMOS RF Power Amplifier With a 2-D Circuit Synthesis Technique. Ding, M., +, TMTT Sept. 2012 2851-2862 Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters. Hoversten, J., +, TMTT June 2012 2010-2020 Digital Predistortion Using a Vector-Switched Model. Afsardoost, S., +, TMTT April 2012 1166-1174 Optimized Low-Complexity Implementation of Least Squares Based Model Extraction for Digital Predistortion of RF Power Amplifiers. Guan, L., +, TMTT March 2012 594-603 Peak-Power Controlling Technique for Enhancing Digital Pre-Distortion of RF Power Amplifiers. Nader, C., +, TMTT Nov. 2012 3571-3581 Radiofrequency identification A Novel Carrier Leakage Suppression Front-End for UHF RFID Reader. Jung, J.-Y., +, TMTT May 2012 1468-1477 A Novel Compact Printable Dual-Polarized Chipless RFID System. Islam, M. A., +, TMTT July 2012 2142-2151 A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading. Koswatta, R. V., +, TMTT Sept. 2012 2925-2933 Design of Compact and Auto-Compensated Single-Layer Chipless RFID Tag. Vena, A., +, TMTT Sept. 2012 2913-2924 Development of Optically Transparent Ultrathin Microwave Absorber for Ultrahigh-Frequency RF Identification System. Okano, Y., +, TMTT Aug. 2012 2456-2464 On the Detection of Frequency-Spectra-Based Chipless RFID Using UWB Impulsed Interrogation. Kalansuriya, P., +, TMTT Dec. 2012 4187-4197 Passive Wireless Temperature Sensor Based on Time-Coded UWB Chipless RFID Tags. Girbau, D., +, TMTT Nov. 2012 3623-3632 Pulse-Biased Low-Power Low-Phase-Noise UHF LC-QVCO for 866 MHz RFID Front-End. Li, J., +, TMTT Oct. 2012 3120-3125 Quadrature Amplitude Modulated Backscatter in Passive and Semipassive UHF RFID Systems. Thomas, S. J., +, TMTT April 2012 1175-1182 Simple Test and Modeling of RFID Tag Backscatter. Kuester, D. G., +, TMTT July 2012 2248-2258 Radiofrequency integrated circuits 2011 RFIC Symposium Mini-Special Issue Editorial. Ponchak, G. E., +, TMTT May 2012 1185

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60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 A CMOS Power Amplifier With a Built-In RF Predistorter for Handset Applications. Son, K. Y., +, TMTT Aug. 2012 2571-2580 A High Dynamic-Range RF Programmable-Gain Front End for G.hn RF-Coax in 65-nm CMOS. Trulls, X., +, TMTT Oct. 2012 3243-3253 A Highly Linear and Efficient CMOS RF Power Amplifier With a 2-D Circuit Synthesis Technique. Ding, M., +, TMTT Sept. 2012 2851-2862 A Phased Array RFIC With Built-In Self-Test Capabilities. Inac, O., +, TMTT Jan. 2012 139-148 An All-Metal Micro-Relay With Bulk Foil Pt–Rh Contacts for High-Power RF Applications. Ozkeskin, F. M., +, TMTT June 2012 1595-1604 Guest Editorial. Popovic, Z., +, TMTT June 2012 1753-1754 in the Modeling Inductive Behavior of MOSFET Scattering Parameter Breakdown Regime. Lee, C.-I., +, TMTT March 2012 502-508 Radiofrequency measurement An Open-Loop Half-Quadrature Hybrid for Multiphase Signals Generation. Chen, H.-S., +, TMTT Jan. 2012 131-138 Passive Wireless Temperature Sensor Based on Time-Coded UWB Chipless RFID Tags. Girbau, D., +, TMTT Nov. 2012 3623-3632 Robust Analog Canceller for High-Dynamic-Range Radio Frequency Measurement. Wetherington, J. M., +, TMTT June 2012 1709-1719 Radiometers -Band Total Power Radiometer Performance Optimization in an SiGe HBT Technology. Dacquay, E., +, TMTT March 2012 813-826 Radiometry Low-Frequency Noise Sources and Gain Stability in Microwave Amplifiers for Radiometry. Gonneau, E., +, TMTT Aug. 2012 2616-2621 Radiotelescopes Wideband CMOS Amplification Stage for a Direct-Sampling Square Kilometre Array Receiver. Navaratne, D., +, TMTT Oct. 2012 3179-3188 Radiowave propagation Diffraction in mm and Sub-mm Wave Indoor Propagation Channels. Jacob, M., +, TMTT March 2012 833-844 Random variables Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides. Ochoa, J. S., +, TMTT Dec. 2012 3919-3926 Ray tracing Diffraction in mm and Sub-mm Wave Indoor Propagation Channels. Jacob, M., +, TMTT March 2012 833-844 Receivers 0.6–3-GHz Wideband Receiver RF Front-End With a Feedforward Noise and Distortion Cancellation Resistive-Feedback LNA. Wang, X., +, TMTT Feb. 2012 387-392 245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology. Mao, Y., +, TMTT Dec. 2012 3823-3833 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin. Ziegler, V., +, TMTT Dec. 2012 4209-4219 Sensitivity of a Passive Correlation Interferometer to an Angularly Moving Source. Nanzer, J. A., +, TMTT Dec. 2012 3868-3876 Receiving antennas 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 A Compact 3-D Harmonic Repeater for Passive Wireless Sensing. Nassar, I. T., +, TMTT Oct. 2012 3309-3316 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 On the Detection of Frequency-Spectra-Based Chipless RFID Using UWB Impulsed Interrogation. Kalansuriya, P., +, TMTT Dec. 2012 4187-4197 Reconfigurable architectures A 0.01–8-GHz (12.5 Gb/s) 4 4 CMOS Switch Matrix. Shin, D., +, TMTT Feb. 2012 381-386 + Check author entry for coauthors

Reconfigurable Dual-Channel Multiband RF Receiver for GPS/ Galileo/BD-2 Systems. Chen, D., +, TMTT Nov. 2012 3491-3501 Rectangular waveguides A Comprehensive Analysis of the Absorption Spectrum of Conducting Ferromagnetic Wires. Liberal, I., +, TMTT July 2012 2055-2065 A Temperature-Compensation Technique for Substrate Integrated Waveguide Cavities and Filters. Djerafi, T., +, TMTT Aug. 2012 2448-2455 Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses. Arnedo, I., +, TMTT May 2012 1244-1257 Theoretical Design and Analysis for – Rectangular Waveguide Mode Converters. Zhang, Q., +, TMTT April 2012 1018-1026 Rectennas Low-Power Wireless Power Delivery. Falkenstein, E., +, TMTT July 2012 2277-2286 Reduced order systems Experimental Characterization of Oscillator Circuits for Reduced-Order Models. Umpierrez, P., +, TMTT Nov. 2012 3527-3541 Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT March 2012 405-418 Reflectometers Formulation for Complete and Accurate Calibration of Six-Port Reflectometer. Haddadi, K., +, TMTT March 2012 574-581 Refractive index Comments on "A Unique Extraction of Metamaterial Parameters Based on Kramers-Kronig Relationship". Barroso, J. J., +, TMTT June 2012 17431744 Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Polarization-Independent Metamaterial Analog of Electromagnetically Induced Transparency for a Refractive-Index-Based Sensor. Meng, F.-Y., +, TMTT Oct. 2012 3013-3022 Regression analysis A 3-D Table-Based Method for Non-Quasi-Static Microwave FET Devices Modeling. Long, Y., +, TMTT Oct. 2012 3088-3095 Relaxation theory Longitudinal-Partitioning-Based Waveform Relaxation Algorithm for Efficient Analysis of Distributed Transmission-Line Networks. Roy, S., +, TMTT March 2012 451-463 Reliability A High-Reliability High-Linearity High-Power RF MEMS Metal-Contact Switch for DC–40-GHz Applications. Patel, C. D., +, TMTT Oct. 2012 3096-3112 Buried Object Characterization Using Ultra-Wideband Ground Penetrating Radar. Li, L., +, TMTT Aug. 2012 2654-2664 Simulation and Measurement of the -Parameters of Obstacles in Periodic Waveguides. Navarro-Tapia, M., +, TMTT April 2012 1146-1155 Resistance Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range. Voinigescu, S. P., +, TMTT Dec. 2012 4024-4034 High-Quality-Factor Active Capacitors for Millimeter-Wave Applications. Ghadiri, A., +, TMTT Dec. 2012 3710-3718 Theory and Design of Class-J Power Amplifiers With Dynamic Load Modulation. Andersson, C. M., +, TMTT Dec. 2012 3778-3786 Resistors An Analytical Formulation for Black Box Conversion Matrix Extraction. Kheirdoost, A., +, TMTT June 2012 1493-1499 An Improved Wideband All-Pass I/Q Network for Millimeter-Wave Phase Shifters. Kim, S. Y., +, TMTT Nov. 2012 3431-3439 Generalization and Reduction of Line-Series-Shunt Calibration for Broadband GaAs and CMOS On-Wafer Scattering Parameter Measurements. Huang, C.-C., +, TMTT Dec. 2012 4138-4144 Resonance Broadband Electromagnetic Modeling of Woven Fabric Composites. Mirotznik, M. S., +, TMTT Jan. 2012 158-169 Resonant frequency A -Band Fully Tunable Cavity Filter. Yassini, B., +, TMTT Dec. 2012 4002-4012 Analysis and Design of Low Phase-Noise Oscillators With Nonlinear Resonators. Imani, A., +, TMTT Dec. 2012 3749-3760

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Design and Analysis of Digital-Assisted Bandwidth-Enhanced Miller Divider in 0.18- m CMOS Process. Kuo, Y.-H., +, TMTT Dec. 2012 37693777 -Mode Dielectric Resonator Filters Using MulInline Pseudoelliptic tiple Evanescent Modes to Selectively Bypass Orthogonal Resonators. Bastioli, S., +, TMTT Dec. 2012 3988-4001 Multistage Directional Filter Based on Band-Reject Filter With Isolation Improvement Using Composite Right-/Left-Handed Transmission Lines. Sun, J. S., +, TMTT Dec. 2012 3950-3958 Passive Subharmonic Generation Using Memoryless Nonlinear Circuits. Safarian, Z., +, TMTT Dec. 2012 4053-4065 Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity. Ruiz-Cruz, J. A., +, TMTT Dec. 2012 3969-3979 Wideband Dual-Mode Microstrip Filter Using Short-Ended Resonator With Centrally Loaded Inductive Stub. Sun, S.-J., +, TMTT Dec. 2012 3667-3673 Widely Tunable High-Efficiency Power Amplifier With Ultra-Narrow Instantaneous Bandwidth. Chen, K., +, TMTT Dec. 2012 3787-3797 Resonator filters A -Band Fully Tunable Cavity Filter. Yassini, B., +, TMTT Dec. 2012 4002-4012 A Broadband and Vialess Vertical Microstrip-to-Microstrip Transition. Huang, X., +, TMTT April 2012 938-944 A Broadband U-Slot Coupled Microstrip-to-Waveguide Transition. Huang, X., +, TMTT May 2012 1210-1217 A Narrowband CMOS Ring Resonator Dual-Mode Active Bandpass Filter With Edge Periphery of 2% Free-Space Wavelength. Su, L., +, TMTT June 2012 1605-1616 A Quasi Elliptic Function 1.75–2.25 GHz 3-Pole Bandpass Filter With Bandwidth Control. Chiou, Y.-C., +, TMTT Feb. 2012 244-249 A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 A Tunable Combline Bandpass Filter Loaded With Series Resonator. Wang, X.-G., +, TMTT June 2012 1569-1576 Common-Mode Suppression in Microstrip Differential Lines by Means of Complementary Split Ring Resonators: Theory and Applications. Naqui, J., +, TMTT Oct. 2012 3023-3034 Design and Analysis of a Tri-Band Dual-Mode Chip Filter for 60-, 77-, and 100-GHz Applications. Yang, C.-L., +, TMTT April 2012 989-997 Design and Diagnosis of Wideband Coupled-Resonator Bandpass Filters. Lee, H.-M., +, TMTT May 2012 1266-1277 Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators. Ahn, H.-R., +, TMTT June 2012 1549-1559 Dual-Mode Ring Resonator Bandpass Filter With Asymmetric Inductive Coupling and Its Miniaturization. Lin, T.-W., +, TMTT Sept. 2012 28082814 Extended Passband Bandstop Filter Cascade With Continuous 0.85–6.6-GHz Coverage. Naglich, E. J., +, TMTT Jan. 2012 21-30 Formal Expression of Sensitivity and Energy Relationship in the Context of the Coupling Matrix. Martinez-Mendoza, M., +, TMTT Nov. 2012 33693375 Intrinsically Switched Varactor-Tuned Filters and Filter Banks. Guyette, A. C., +, TMTT April 2012 1044-1056 Lumped-Element Realization of Absorptive Bandstop Filter With Anomalously High Spectral Isolation. Lee, J., +, TMTT Aug. 2012 2424-2430 Novel Second-Order Dual-Mode Dual-Band Filters Using Capacitance Loaded Square Loop Resonator. Fu, S., +, TMTT March 2012 477-483 Switchless Tunable Bandstop-to-All-Pass Reconfigurable Filter. Naglich, E. J., +, TMTT May 2012 1258-1265 Wideband Dual-Mode Microstrip Filter Using Short-Ended Resonator With Centrally Loaded Inductive Stub. Sun, S.-J., +, TMTT Dec. 2012 3667-3673 Resonators A CMOS Noise-Squeezing Amplifier. Lee, W., +, TMTT Feb. 2012 329-339 A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the Turnstile Waveguide Circulator. Helszajn, J., +, TMTT Oct. 2012 3079-3087 Authors’ Reply to “Comments on Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship”. Szabo, Z., +, TMTT Nov. 2012 3634-3635 Comments on "A Unique Extraction of Metamaterial Parameters Based on Kramers-Kronig Relationship". Barroso, J. J., +, TMTT June 2012 17431744

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4285

Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Dual Composite Right-/Left-Handed Coplanar Waveguide Transmission Line Using Inductively Connected Split-Ring Resonators. Belenguer, A., +, TMTT Oct. 2012 3035-3042 Highly Miniaturized Multiband Bandpass Filter Design Based on a Stacked Spiral Resonator Structure. Chen, C.-H., +, TMTT May 2012 1278-1286 Microstrip Bandpass Filters With Various Resonators Using Connected- and Edge-Coupling Mechanisms and Their Applications to Dual-Band Filters and Diplexers. Lin, S.-C., +, TMTT April 2012 975-988 Novel Coupling Structure for the Resonant Coaxial Probe. Rowe, D. J., +, TMTT June 2012 1699-1708 Polarization-Independent Metamaterial Analog of Electromagnetically Induced Transparency for a Refractive-Index-Based Sensor. Meng, F.-Y., +, TMTT Oct. 2012 3013-3022 Pseudo-Traveling-Wave Resonator With Magnetically Tunable Phase Gradient of Fields and Its Applications to Beam-Steering Antennas. Ueda, T., +, TMTT Oct. 2012 3043-3054 Ring-Resonator-Inspired Power Recycling Scheme for Gain-Enhanced Distributed Amplifier-Based CRLH-Transmission Line Leaky Wave Antennas. Wu, C.-T. M., +, TMTT April 2012 1027-1037 Stepped-Impedance Coupled Resonators for Implementation of Parallel Coupled Microstrip Filters With Spurious Band Suppression. Worapishet, A., +, TMTT June 2012 1540-1548 Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control. Serrano, A. L. C., +, TMTT March 2012 484-493 RF signals High-Gain and High-Efficiency EER/Polar Transmitters Using InjectionLocked Oscillators. Chen, C.-T., +, TMTT Dec. 2012 4117-4128 Rhodium alloys An All-Metal Micro-Relay With Bulk Foil Pt–Rh Contacts for High-Power RF Applications. Ozkeskin, F. M., +, TMTT June 2012 1595-1604 Ridge waveguides A Broadband U-Slot Coupled Microstrip-to-Waveguide Transition. Huang, X., +, TMTT May 2012 1210-1217 Road vehicle radar A 24-GHz CMOS UWB Radar Transmitter With Compressed Pulses. Yang, J., +, TMTT April 2012 1117-1125 A Transformer-Coupling Current-Reuse SiGe HBT Power Amplifier for 77-GHz Automotive Radar. Giammello, V., +, TMTT June 2012 1676-1683 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Millimeter-Wave Technology for Automotive Radar Sensors in the 77 GHz Frequency Band. Hasch, J., +, TMTT March 2012 845-860

S S-matrix theory A New Balanced-to-Balanced Power Divider/Combiner. Xia, B., +, TMTT Sept. 2012 2791-2798 S-parameters A New Balanced-to-Balanced Power Divider/Combiner. Xia, B., +, TMTT Sept. 2012 2791-2798 Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures. Dadash, M. S., +, TMTT Sept. 2012 2713-2722 Broadband 90 Differential Phase Shifter Constructed Using a Pair of Multisection Radial Line Stubs. Yeung, S. H., +, TMTT Sept. 2012 2760-2767 Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators. Ahn, H.-R., +, TMTT June 2012 1549-1559 Device Characterization Techniques Based on Causal Relationships. Wojnowski, M., +, TMTT July 2012 2203-2219 Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies. Bayatpur, F., +, TMTT April 2012 1126-1135 Experimental Validation of Frozen Modes Guided on Printed Coupled Transmission Lines. Apaydin, N., +, TMTT June 2012 1513-1519 Fast and Efficient Analysis of Transmission Lines With Arbitrary Nonuniformities of Sub-Wavelength Scale. Javadzadeh, S. M. H., +, TMTT Aug. 2012 2378-2384 -Band CMOS Chip Modules on Ceramic InteFlip-Chip-Assembled grated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777

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Formal Expression of Sensitivity and Energy Relationship in the Context of the Coupling Matrix. Martinez-Mendoza, M., +, TMTT Nov. 2012 33693375 Graphical Analysis of Stabilization Loss and Gains for Three-Port Networks. Tan, E. L., +, TMTT June 2012 1635-1640 Large-Signal Oscillator Design Procedure Utilizing Analytical -Parameters Closed-Form Expressions. Pelaez-Perez, A. M., +, TMTT Oct. 2012 3126-3136 in the Modeling Inductive Behavior of MOSFET Scattering Parameter Breakdown Regime. Lee, C.-I., +, TMTT March 2012 502-508 Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements. Hu, F.-G., +, TMTT July 2012 2046-2054 Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation. Kilic, E., +, TMTT May 2012 14371443 Simulation and Measurement of the -Parameters of Obstacles in Periodic Waveguides. Navarro-Tapia, M., +, TMTT April 2012 1146-1155 Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates. Evseev, S. B., +, TMTT Nov. 2012 3542-3550 Satellite antennas 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules. Florian, C., +, TMTT June 2012 1805-1816 Scattering Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings. Memarian, M., +, TMTT Dec. 2012 3893-3907 Schottky diode mixers 60-GHz Dual-Conversion Down-/Up-Converters Using Schottky Diode in 0.18 m Foundry CMOS Technology. Wei, H.-J., +, TMTT June 2012 16841698 A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 Schottky diodes Low-Power Wireless Power Delivery. Falkenstein, E., +, TMTT July 2012 2277-2286 Secondary emission Prediction of Multipactor Breakdown for Multicarrier Applications: The Quasi-Stationary Method. Anza, S., +, TMTT July 2012 2093-2105 Security Security Pre-screening of Moving Persons Using a Rotating Multichannel -Band Radar. Hantscher, S., +, TMTT March 2012 870-880 Semiconductor device breakdown in the Modeling Inductive Behavior of MOSFET Scattering Parameter Breakdown Regime. Lee, C.-I., +, TMTT March 2012 502-508 Semiconductor device measurement Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates. Evseev, S. B., +, TMTT Nov. 2012 3542-3550 Semiconductor device metallization Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels. Calafiore, G. C., +, TMTT Oct. 2012 2990-3003 Semiconductor device models A 3-D Table-Based Method for Non-Quasi-Static Microwave FET Devices Modeling. Long, Y., +, TMTT Oct. 2012 3088-3095 Microwave and RF p-i-n Diode Model for Time-Domain Simulation. Caverly, R. H., +, TMTT July 2012 2158-2164 in the Modeling Inductive Behavior of MOSFET Scattering Parameter Breakdown Regime. Lee, C.-I., +, TMTT March 2012 502-508 New Trends for the Nonlinear Measurement and Modeling of High-Power RF Transistors and Amplifiers With Memory Effects. Roblin, P., +, TMTT June 2012 1964-1978 Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels. Calafiore, G. C., +, TMTT Oct. 2012 2990-3003 Systematic Compact Modeling of Correlated Noise in Bipolar Transistors. Herricht, J., +, TMTT Nov. 2012 3403-3412 Two-Way Current-Combining -Band Power Amplifier in 65-nm CMOS. Gu, Q. J., +, TMTT May 2012 1365-1374 Semiconductor device noise Systematic Compact Modeling of Correlated Noise in Bipolar Transistors. Herricht, J., +, TMTT Nov. 2012 3403-3412

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Semiconductor device packaging Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels. Calafiore, G. C., +, TMTT Oct. 2012 2990-3003 Semiconductor device reliability Design-in-Reliable Millimeter-Wave Power Amplifiers in a 65-nm CMOS Process. Quemerais, T., +, TMTT April 2012 1079-1085 Semiconductor switches Ultrafast Low-Loss 42–70 GHz Differential SPDT Switch in 0.35 m SiGe Technology. Thian, M., +, TMTT March 2012 655-659 Semiconductor technology Multimode TRL Calibration Technique for Characterization of Differential Devices. Wojnowski, M., +, TMTT July 2012 2220-2247 Semiconductor-insulator boundaries -Band Amplifiers With 6-dB Noise Figure and Milliwatt-Level 170–200-GHz Doublers in 45-nm CMOS. Cetinoneri, B., +, TMTT March 2012 692-701 Sensitivity Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures. Dadash, M. S., +, TMTT Sept. 2012 2713-2722 Generalized Time-Domain Adjoint Sensitivity Analysis of Distributed MTL Networks. Saini, A. S., +, TMTT Nov. 2012 3359-3368 On the Relation Between Stored Energy and Fabrication Tolerances in Microwave Filters. Martinez-Mendoza, M., +, TMTT July 2012 2131-2141 Sensitivity of a Passive Correlation Interferometer to an Angularly Moving Source. Nanzer, J. A., +, TMTT Dec. 2012 3868-3876 Sensors A 1–8-GHz Miniaturized Spectroscopy System for Permittivity Detection and Mixture Characterization of Organic Chemicals. Helmy, A. A., +, TMTT Dec. 2012 4157-4170 Accurate Nanoliter Liquid Characterization Up to 40 GHz for Biomedical Applications: Toward Noninvasive Living Cells Monitoring. Chen, T., +, TMTT Dec. 2012 4171-4177 Shot noise Systematic Compact Modeling of Correlated Noise in Bipolar Transistors. Herricht, J., +, TMTT Nov. 2012 3403-3412 Signal generators A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator. Lee, S., +, TMTT May 2012 1405-1412 An Open-Loop Half-Quadrature Hybrid for Multiphase Signals Generation. Chen, H.-S., +, TMTT Jan. 2012 131-138 Millimeter-Wave Optoelectronic Mixers Based on Uni-Traveling Carrier Photodiodes. Rouvalis, E., +, TMTT March 2012 686-691 Peak-Power Controlling Technique for Enhancing Digital Pre-Distortion of RF Power Amplifiers. Nader, C., +, TMTT Nov. 2012 3571-3581 Signal processing Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters. Hoversten, J., +, TMTT June 2012 2010-2020 Signal resolution Analog Signal Processing for Pulse Compression Radar in 90-nm CMOS. Parlak, M., +, TMTT Dec. 2012 3810-3822 Silicon 60-GHz Dual-Conversion Down-/Up-Converters Using Schottky Diode in 0.18 m Foundry CMOS Technology. Wei, H.-J., +, TMTT June 2012 16841698 A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 CMOS Integrated Antenna-Coupled Field-Effect Transistors for the Detection of Radiation From 0.2 to 4.3 THz. Boppel, S., +, TMTT Dec. 2012 3834-3843 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process. Lin, C.-Y., +, TMTT March 2012 714-723 Guest Editorial. Rieh, J.-S., +, TMTT Dec. 2012 3641 Miniaturized UWB Filters Integrated With Tunable Notch Filters Using a Silicon-Based Integrated Passive Device Technology. Wu, Z., +, TMTT March 2012 518-527 Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates. Evseev, S. B., +, TMTT Nov. 2012 3542-3550 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Silicon compounds A Four-Channel 94-GHz SiGe-Based Digital Beamforming FMCW Radar. Jahn, M., +, TMTT March 2012 861-869 A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer. Pohl, N., +, TMTT March 2012 757-765 Design and Analysis of Down-Conversion Gate/Base-Pumped Harmonic Mixers Using Novel Reduced-Size 180 Hybrid With Different Input Frequencies. Kuo, J.-J., +, TMTT Aug. 2012 2473-2485 Subharmonic 220- and 320-GHz SiGe HBT Receiver Front-Ends. Ojefors, E., +, TMTT May 2012 1397-1404 Silicon germanium An Ultra-Thin, High-Power, and Multilayer Organic Antenna Array With T/R Functionality in the -Band. Donado Morcillo, C. A., +, TMTT Dec. 2012 3856-3867 Characterization and Modeling of an SiGe HBT Technology for Transceiver Applications in the 100–300-GHz Range. Voinigescu, S. P., +, TMTT Dec. 2012 4024-4034 Guest Editorial. Rebeiz, G. M., +, TMTT March 2012 637-639 Silicon-on-insulator -Band and -Band Power Amplifiers in 45-nm CMOS SOI. Kim, J., +, TMTT June 2012 1870-1877 High-Efficiency Cellular Power Amplifiers Based on a Modified LDMOS Process on Bulk Silicon and Silicon-On-Insulator Substrates With Integrated Power Management Circuitry. Tombak, A., +, TMTT June 2012 1862-1869 Singular value decomposition Authors’ reply. Chen, G., +, TMTT June 2012 1745-1747 Skin Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 New Method for Determining Dielectric Properties of Skin and Phantoms at Millimeter Waves Based on Heating Kinetics. Chahat, N., +, TMTT March 2012 827-832 Skin effect A Comprehensive Analysis of the Absorption Spectrum of Conducting Ferromagnetic Wires. Liberal, I., +, TMTT July 2012 2055-2065 Slot antenna arrays Broadband Millimeter-Wave Single Balanced Mixer and Its Applications to Substrate Integrated Wireless Systems. Zhang, Z.-Y., +, TMTT March 2012 660-669 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Multilayer Antenna-Filter Antenna for Beam-Steering Transmit-Array Applications. Boccia, L., +, TMTT July 2012 2287-2300 Slot antennas A Novel Compact Printable Dual-Polarized Chipless RFID System. Islam, M. A., +, TMTT July 2012 2142-2151 Slot line components Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter. Lin, F., +, TMTT May 2012 1226-1234 Slot lines Comments on "Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter". Sun, Z., +, TMTT Sept. 2012 2934 Slow wave structures A High Slow-Wave Factor Microstrip Structure With Simple Design Formulas and Its Application to Microwave Circuit Design. Chang, W.-S., +, TMTT Nov. 2012 3376-3383 High-Performance Solenoidal RF Transformers on High-Resistivity Silicon Substrates for 3D Integrated Circuits. Feng, Z., +, TMTT July 2012 20662072 Software radio 24-GHz Integrated Radio and Radar System Capable of Time-Agile Wireless Communication and Sensing. Han, L., +, TMTT March 2012 619-631 A 130-nm CMOS 100-Hz–6-GHz Reconfigurable Vector Signal Analyzer and Software-Defined Receiver. Goel, A., +, TMTT May 2012 1375-1389 Vectorially Combined Distributed Power Amplifiers for Software-Defined Radio Applications. Narendra, K., +, TMTT Oct. 2012 3189-3200

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4287

Solenoids High-Performance Solenoidal RF Transformers on High-Resistivity Silicon Substrates for 3D Integrated Circuits. Feng, Z., +, TMTT July 2012 20662072 Solid modeling A Novel Model for Implementation of Gamma Radiation Effects in GaAs HBTs. Zhang, J., +, TMTT Dec. 2012 3693-3698 Special issues and sections 2011 RFIC Symposium Mini-Special Issue Editorial. Ponchak, G. E., +, TMTT May 2012 1185 Guest Editorial. Rebeiz, G. M., +, TMTT March 2012 637-639 Guest Editorial. Popovic, Z., +, TMTT June 2012 1753-1754 Guest Editorial. Rieh, J.-S., +, TMTT Dec. 2012 3641 Guest Editorial. Lin, F., +, TMTT Nov. 2012 3347-3348 Spectral analysers A 130-nm CMOS 100-Hz–6-GHz Reconfigurable Vector Signal Analyzer and Software-Defined Receiver. Goel, A., +, TMTT May 2012 1375-1389 Spectral-domain analysis Rigorous Derivation and Fast Solution of Spatial-Domain Green’s Functions for Uniaxial Anisotropic Multilayers Using Modified Fast Hankel Transform Method. Ding, P.-P., +, TMTT Feb. 2012 205-217 Spectroscopy A 1–8-GHz Miniaturized Spectroscopy System for Permittivity Detection and Mixture Characterization of Organic Chemicals. Helmy, A. A., +, TMTT Dec. 2012 4157-4170 SPICE SPICE Lumped Circuit Subcell Model for the Discontinuous Galerkin Finite-Element Time-Domain Method. Zhao, B., +, TMTT Sept. 2012 26842692 Stability Experimental Characterization of Stability Margins in Microwave Amplifiers. Otegi, N., +, TMTT Dec. 2012 4145-4156 Graphical Analysis of Stabilization Loss and Gains for Three-Port Networks. Tan, E. L., +, TMTT June 2012 1635-1640 Standards Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier Using In-Band Continuous Class-F F Mode Transferring. Chen, K., +, TMTT Dec. 2012 4107-4116 Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides. Ochoa, J. S., +, TMTT Dec. 2012 3919-3926 Triple-Conductor Combline Resonators for Dual-Band Filters With Enhanced Guard-Band Selectivity. Ruiz-Cruz, J. A., +, TMTT Dec. 2012 3969-3979 Statistical analysis 120-GHz-Band Wireless Link Technologies for Outdoor 10-Gbit/s Data Transmission. Hirata, A., +, TMTT March 2012 881-895 Optimized Low-Complexity Implementation of Least Squares Based Model Extraction for Digital Predistortion of RF Power Amplifiers. Guan, L., +, TMTT March 2012 594-603 Portable Space Mapping for Efficient Statistical Modeling of Passive Components. Zhang, L., +, TMTT March 2012 441-450 Steady-state Analysis and Design of Low Phase-Noise Oscillators With Nonlinear Resonators. Imani, A., +, TMTT Dec. 2012 3749-3760 Passive Subharmonic Generation Using Memoryless Nonlinear Circuits. Safarian, Z., +, TMTT Dec. 2012 4053-4065 Stochastic processes Analysis and Design of Low Phase-Noise Oscillators With Nonlinear Resonators. Imani, A., +, TMTT Dec. 2012 3749-3760 Stress analysis Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 Strip line resonators A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 Design of Compact and Auto-Compensated Single-Layer Chipless RFID Tag. Vena, A., +, TMTT Sept. 2012 2913-2924 Strip lines Novel Dual-Band Out-of-Phase Power Divider With High Power-Handling Capability. Dai, G.-L., +, TMTT Aug. 2012 2403-2409 Substrate Integrated Waveguide Quasi-Elliptic Filters With Controllable Electric and Magnetic Mixed Coupling. Gong, K., +, TMTT Oct. 2012 3071-3078

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Stripline An Ultra-Thin, High-Power, and Multilayer Organic Antenna Array With T/R Functionality in the -Band. Donado Morcillo, C. A., +, TMTT Dec. 2012 3856-3867 Strips A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide. Lee, J.-W., +, TMTT Dec. 2012 3642-3655 Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings. Memarian, M., +, TMTT Dec. 2012 3893-3907 Strontium compounds A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 Submillimeter wave amplifiers Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 Submillimeter wave antennas Optical Modulation of Millimeter-Wave Beams Using a Semiconductor Substrate. Gallacher, T. F., +, TMTT July 2012 2301-2309 Submillimeter wave devices Crosstalk Reduction for Superconducting Microwave Resonator Arrays. Noroozian, O., +, TMTT May 2012 1235-1243 Submillimeter wave integrated circuits Terahertz Micromachined On-Wafer Probes: Repeatability and Reliability. Chen, L., +, TMTT Sept. 2012 2894-2902 Submillimeter wave mixers Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 Submillimeter wave receivers Low-Power Very Low-Noise Cryogenic SiGe IF Amplifiers for Terahertz Mixer Receivers. Russell, D., +, TMTT June 2012 1641-1648 Submillimeter waves Nonperiodic Perturbations in Periodic RF Structures. Jabotinski, V., +, TMTT April 2012 915-929 Substrate integrated waveguides 24-GHz Integrated Radio and Radar System Capable of Time-Agile Wireless Communication and Sensing. Han, L., +, TMTT March 2012 619-631 A Temperature-Compensation Technique for Substrate Integrated Waveguide Cavities and Filters. Djerafi, T., +, TMTT Aug. 2012 2448-2455 Broadband Millimeter-Wave Single Balanced Mixer and Its Applications to Substrate Integrated Wireless Systems. Zhang, Z.-Y., +, TMTT March 2012 660-669 Efficient Analysis of Metallic and Dielectric Posts in Parallel-Plate Waveguide Structures. Casaletti, M., +, TMTT Oct. 2012 2979-2989 Efficient Analysis of Substrate Integrated Waveguide Devices Using Hybrid Mode Matching Between Cylindrical and Guided Modes. Diaz Caballero, E., +, TMTT Feb. 2012 232-243 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Millimeter-Wave Printed Circuit Board Characterization Using Substrate Integrated Waveguide Resonators. Zelenchuk, D. E., +, TMTT Oct. 2012 3300-3308 Mode Analysis of the Corrugated Substrate Integrated Waveguide. Eccleston, K. W., +, TMTT Oct. 2012 3004-3012 Substrate Integrated Waveguide Quasi-Elliptic Filters With Controllable Electric and Magnetic Mixed Coupling. Gong, K., +, TMTT Oct. 2012 3071-3078 Ultra-Wideband Single and Dual Baluns Based on Substrate Integrated Coaxial Line Technology. Zhu, F., +, TMTT Oct. 2012 3062-3070 Substrates A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN. Chen, J.-H., +, TMTT Dec. 2012 4089-4096 An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications. Kim, S., +, TMTT Dec. 2012 4178-4186 An Ultra-Thin, High-Power, and Multilayer Organic Antenna Array With T/R Functionality in the -Band. Donado Morcillo, C. A., +, TMTT Dec. 2012 3856-3867 Superheterodyne receivers Direct Baseband I-Q Regeneration Method for Five-Port Receivers Improving DC-Offset and Second-Order Intermodulation Distortion Rejection. de la Morena-Alvarez-Palencia, C., +, TMTT Aug. 2012 2634-2643

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Surface acoustic wave filters Compact Vital Signal Sensor Using Oscillation Frequency Deviation. Kim, S.-G., +, TMTT Feb. 2012 393-400 Surface impedance FDTD Modeling of Impedance Boundary Conditions by Equivalent LTI Circuits. Feliziani, M., +, TMTT Dec. 2012 3656-3666 Surface resistance Surface-Charge-Layer Sheet-Resistance Measurements for Evaluating Interface RF Losses on High-Resistivity-Silicon Substrates. Evseev, S. B., +, TMTT Nov. 2012 3542-3550 Surface waves Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave. Wu, J., +, TMTT Dec. 2012 3959-3968 Surveillance Development of Optically Transparent Ultrathin Microwave Absorber for Ultrahigh-Frequency RF Identification System. Okano, Y., +, TMTT Aug. 2012 2456-2464 Switched capacitor networks A Dual-Mode CMOS RF Power Amplifier With Integrated Tunable Matching Network. Yoon, Y., +, TMTT Jan. 2012 77-88 Switched filters Intrinsically Switched Varactor-Tuned Filters and Filter Banks. Guyette, A. C., +, TMTT April 2012 1044-1056 Switched mode power supplies Modulator for Switch-Mode Power A 5-Gb/s 2.1–2.2-GHz Bandpass Amplifier. Ostrovskyy, P., +, TMTT Aug. 2012 2524-2531 Switches 180 and 90 Reflection-Type Phase Shifters Using Over-Coupled Lange Couplers. Fang, H. R., +, TMTT Nov. 2012 3440-3448 A 7.9-mW 5.6-GHz Digitally Controlled Variable Gain Amplifier With Linearization. Kumar, T. B., +, TMTT Nov. 2012 3482-3490 Design and Analysis of Digital-Assisted Bandwidth-Enhanced Miller Divider in 0.18- m CMOS Process. Kuo, Y.-H., +, TMTT Dec. 2012 37693777 High-Gain and High-Efficiency EER/Polar Transmitters Using InjectionLocked Oscillators. Chen, C.-T., +, TMTT Dec. 2012 4117-4128 Synchronization Analysis of the Locking Range of Rationally Synchronized Oscillators With High Reference Signal Power. Fernandez Garcia, M., +, TMTT Aug. 2012 2494-2504 Synthesizers A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer. Tang, A., +, TMTT Dec. 2012 4129-4137 Synthetic aperture radar 12-W -Band MMIC HPA and Driver Amplifiers in InGaP-GaAs HBT Technology for Space SAR T/R Modules. Florian, C., +, TMTT June 2012 1805-1816 System-in-package 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756 A Fully SiP Integrated -Band Butler Matrix End-Fire Beam-Switching Transmitter Using Flip-Chip Assembled CMOS Chips on LTCC. Kuo, C.-C., +, TMTT May 2012 1424-1436 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777 System-on-package A Broadband and Vialess Vertical Microstrip-to-Microstrip Transition. Huang, X., +, TMTT April 2012 938-944 T Telecommunication network management Distortion Mechanisms Originating From Modal Noise in Radio Over Multimode Fiber Links. Alcaro, G., +, TMTT Jan. 2012 185-194 Telescopes Crosstalk Reduction for Superconducting Microwave Resonator Arrays. Noroozian, O., +, TMTT May 2012 1235-1243

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Temperature measurement Multiphysics Modeling of RF and Microwave High-Power Transistors. Aaen, P. H., +, TMTT Dec. 2012 4013-4023 Temperature sensors A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467 Passive Wireless Temperature Sensor Based on Time-Coded UWB Chipless RFID Tags. Girbau, D., +, TMTT Nov. 2012 3623-3632 Terahertz wave devices Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes. Rouvalis, E., +, TMTT March 2012 509-517 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Terahertz wave generation Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes. Rouvalis, E., +, TMTT March 2012 509-517 Thermal expansion A Temperature-Compensation Technique for Substrate Integrated Waveguide Cavities and Filters. Djerafi, T., +, TMTT Aug. 2012 2448-2455 Thermal management (packaging) A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 Thin film capacitors A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 Three-dimensional integrated circuits High-Performance Solenoidal RF Transformers on High-Resistivity Silicon Substrates for 3D Integrated Circuits. Feng, Z., +, TMTT July 2012 20662072 Vertical RF Transition With Mechanical Fit for 3-D Heterogeneous Integration. Chen, L., +, TMTT March 2012 647-654 Thyristors ESD Protection Design for 60-GHz LNA With Inductor-Triggered SCR in 65-nm CMOS Process. Lin, C.-Y., +, TMTT March 2012 714-723 Time domain analysis 24-GHz Integrated Radio and Radar System Capable of Time-Agile Wireless Communication and Sensing. Han, L., +, TMTT March 2012 619-631 A Spurious-Free Discontinuous Galerkin Time-Domain Method for the Accurate Modeling of Microwave Filters. Alvarez, J., +, TMTT Aug. 2012 2359-2369 A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters. Ahmed, O. S., +, TMTT Oct. 2012 2959-2971 FDTD Modeling of Impedance Boundary Conditions by Equivalent LTI Circuits. Feliziani, M., +, TMTT Dec. 2012 3656-3666 Generalized Time-Domain Adjoint Sensitivity Analysis of Distributed MTL Networks. Saini, A. S., +, TMTT Nov. 2012 3359-3368 Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach. Kabir, M., +, TMTT Dec. 2012 3927-3938 Microwave and RF p-i-n Diode Model for Time-Domain Simulation. Caverly, R. H., +, TMTT July 2012 2158-2164 Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements. Hu, F.-G., +, TMTT July 2012 2046-2054 On the Equivalence Between the Maxwell-Garnett Mixing Rule and the Debye Relaxation Formula. Salski, B., +, TMTT Aug. 2012 2352-2358 SPICE Lumped Circuit Subcell Model for the Discontinuous Galerkin Finite-Element Time-Domain Method. Zhao, B., +, TMTT Sept. 2012 26842692 Time varying networks TLM Extension to Electromagnetic Field Analysis of Anisotropic and Dispersive Media: A Unified Field Equation. Farhat, A. L., +, TMTT Aug. 2012 2339-2351 Topology 245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology. Mao, Y., +, TMTT Dec. 2012 3823-3833 Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique. Yeh, H.-C., +, TMTT Dec. 2012 4066-4079 GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion. Garcia, J. A., +, TMTT Dec. 2012 4220-4229

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4289

Inline Pseudoelliptic -Mode Dielectric Resonator Filters Using Multiple Evanescent Modes to Selectively Bypass Orthogonal Resonators. Bastioli, S., +, TMTT Dec. 2012 3988-4001 Narrowband Microwave Filters With Mixed Topology. Macchiarella, G., +, TMTT Dec. 2012 3980-3987 On the Compression and Blocking Distortion of Semiconductor-Based Varactors. Huang, C., +, TMTT Dec. 2012 3699-3709 Transceivers Design and Analysis of Down-Conversion Gate/Base-Pumped Harmonic Mixers Using Novel Reduced-Size 180 Hybrid With Different Input Frequencies. Kuo, J.-J., +, TMTT Aug. 2012 2473-2485 Terahertz Aperture Synthesized Imaging With Fan-Beam Scanning for Personnel Screening. Gu, S., +, TMTT Dec. 2012 3877-3885 Transconductance 245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology. Mao, Y., +, TMTT Dec. 2012 3823-3833 Transducers Nonreciprocal Tunable Low-Loss Bandpass Filters With Ultra-Wideband Isolation Based on Magnetostatic Surface Wave. Wu, J., +, TMTT Dec. 2012 3959-3968 Transfer function matrices Robust Passive Macro-Model Generation With Local Compensation. Wang, T., +, TMTT Aug. 2012 2313-2328 Transfer functions Comments on “Theoretical and Experimental Study of a New Class of Reflectionless Filter”. Roy, S. C. D., +, TMTT March 2012 632-633 CRLH–CRLH C-Section Dispersive Delay Structures With Enhanced Group-Delay Swing for Higher Analog Signal Processing Resolution. Gupta, S., +, TMTT Dec. 2012 3939-3949 Variability Analysis of Multiport Systems Via Polynomial-Chaos Expansion. Spina, D., +, TMTT Aug. 2012 2329-2338 Transformers A 30.8-dBm Wideband CMOS Power Amplifier With Minimized Supply Fluctuation. Jin, B., +, TMTT June 2012 1658-1666 and A Generalized Dual-Band Wilkinson Power Divider With Parallel Components. Wang, X., +, TMTT April 2012 952-964 Design of CMOS Power Amplifiers. Niknejad, A. M., +, TMTT June 2012 1784-1796 Modeling and Digital Predistortion of Class-D Outphasing RF Power Amplifiers. Landin, P. N., +, TMTT June 2012 1907-1915 Unequal Wilkinson Power Dividers With Favorable Selectivity and HighIsolation Using Coupled-Line Filter Transformers. Deng, P.-H., +, TMTT June 2012 1520-1529 Transient analysis Longitudinal-Partitioning-Based Waveform Relaxation Algorithm for Efficient Analysis of Distributed Transmission-Line Networks. Roy, S., +, TMTT March 2012 451-463 Transistor circuits Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes. Suarez, A., +, TMTT March 2012 528-541 Transistors A 64–84-GHz PLL With Low Phase Noise in an 80-GHz SiGe HBT Technology. Liu, G., +, TMTT Dec. 2012 3739-3748 A Wideband RF Power Amplifier in 45-nm CMOS SOI Technology With Substrate Transferred to AlN. Chen, J.-H., +, TMTT Dec. 2012 4089-4096 Analysis and Design of Millimeter-Wave Low-Voltage CMOS Cascode LNA With Magnetic Coupled Technique. Yeh, H.-C., +, TMTT Dec. 2012 4066-4079 Design of Broadband Highly Efficient Harmonic-Tuned Power Amplifier Using In-Band Continuous Class-F F Mode Transferring. Chen, K., +, TMTT Dec. 2012 4107-4116 High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers. Roberg, M., +, TMTT Dec. 2012 4043-4052 High-Quality-Factor Active Capacitors for Millimeter-Wave Applications. Ghadiri, A., +, TMTT Dec. 2012 3710-3718 Multiphysics Modeling of RF and Microwave High-Power Transistors. Aaen, P. H., +, TMTT Dec. 2012 4013-4023 PA Efficiency and Linearity Enhancement Using External Harmonic Injection. Dani, A., +, TMTT Dec. 2012 4097-4106 Theory and Design of Class-J Power Amplifiers With Dynamic Load Modulation. Andersson, C. M., +, TMTT Dec. 2012 3778-3786 Widely Tunable High-Efficiency Power Amplifier With Ultra-Narrow Instantaneous Bandwidth. Chen, K., +, TMTT Dec. 2012 3787-3797

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Transmission line matrix methods Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach. Kabir, M., +, TMTT Dec. 2012 3927-3938 TLM Extension to Electromagnetic Field Analysis of Anisotropic and Dispersive Media: A Unified Field Equation. Farhat, A. L., +, TMTT Aug. 2012 2339-2351 Transmission line measurements 245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology. Mao, Y., +, TMTT Dec. 2012 3823-3833 Multiphysics Modeling of RF and Microwave High-Power Transistors. Aaen, P. H., +, TMTT Dec. 2012 4013-4023 Transmission line theory A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters. Ahmed, O. S., +, TMTT Oct. 2012 2959-2971 Fast and Efficient Analysis of Transmission Lines With Arbitrary Nonuniformities of Sub-Wavelength Scale. Javadzadeh, S. M. H., +, TMTT Aug. 2012 2378-2384 Longitudinal-Partitioning-Based Waveform Relaxation Algorithm for Efficient Analysis of Distributed Transmission-Line Networks. Roy, S., +, TMTT March 2012 451-463 Portable Space Mapping for Efficient Statistical Modeling of Passive Components. Zhang, L., +, TMTT March 2012 441-450 Theory of Magnetic Transmission Lines. Brandao Faria, J. A., +, TMTT Oct. 2012 2941-2949 Transmission lines A 15–50-GHz Quasi-Optical Scalar Network Analyzer Scalable to Terahertz Frequencies. Grichener, A., +, TMTT Aug. 2012 2622-2633 A Dual-Band 10/24-GHz Amplifier Design Incorporating Dual-Frequency Complex Load Matching. Hsieh, K.-A., +, TMTT June 2012 1649-1657 A New Balanced-to-Balanced Power Divider/Combiner. Xia, B., +, TMTT Sept. 2012 2791-2798 Analysis of Composite Right/Left-Handed Unit Cells Based on Even–OddMode Excitation. Eberspacher, M. A., +, TMTT May 2012 1186-1196 Analytical Design Methodology of Outphasing Amplification Systems Using a New Simplified Chireix Combiner Model. El-Asmar, M., +, TMTT June 2012 1886-1895 Application of Stepped-Impedance Technique for Bandwidth Control of Dual-Band Filters. Ha, J., +, TMTT July 2012 2106-2114 Broadband 90 Differential Phase Shifter Constructed Using a Pair of Multisection Radial Line Stubs. Yeung, S. H., +, TMTT Sept. 2012 2760-2767 Common-Mode Suppression in Microstrip Differential Lines by Means of Complementary Split Ring Resonators: Theory and Applications. Naqui, J., +, TMTT Oct. 2012 3023-3034 Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter. Lin, F., +, TMTT May 2012 1226-1234 Complex Impedance Transformers Consisting of Only Transmission-Line Sections. Ahn, H.-R., +, TMTT July 2012 2073-2084 Dual Composite Right-/Left-Handed Coplanar Waveguide Transmission Line Using Inductively Connected Split-Ring Resonators. Belenguer, A., +, TMTT Oct. 2012 3035-3042 Hybrid Field/Transmission-Line Model for the Study of Coaxial Corrugated Waveguides. Savaidis, S. P., +, TMTT Oct. 2012 2972-2978 Switchless Tunable Bandstop-to-All-Pass Reconfigurable Filter. Naglich, E. J., +, TMTT May 2012 1258-1265 Transmitters A -Band CMOS Transmitter With IF-Envelope Feed-Forward Pre-Distortion and Injection-Locked Frequency-Tripling Synthesizer. Tang, A., +, TMTT Dec. 2012 4129-4137 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A 50-Mb/s CMOS QPSK/O-QPSK Transmitter Employing Injection Locking for Direct Modulation. Diao, S., +, TMTT Jan. 2012 120-130 A Single Envelope Modulator-Based Envelope-Tracking Structure for Multiple-Input and Multiple-Output Wireless Transmitters. Yu, C., +, TMTT Oct. 2012 3317-3327 High-Gain and High-Efficiency EER/Polar Transmitters Using InjectionLocked Oscillators. Chen, C.-T., +, TMTT Dec. 2012 4117-4128 Transmitting antennas 60-GHz Four-Element Phased-Array Transmit/Receive System-in-Package Using Phase Compensation Techniques in 65-nm Flip-Chip CMOS Process. Kuo, J.-L., +, TMTT March 2012 743-756

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A Compact 3-D Harmonic Repeater for Passive Wireless Sensing. Nassar, I. T., +, TMTT Oct. 2012 3309-3316 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Multilayer Antenna-Filter Antenna for Beam-Steering Transmit-Array Applications. Boccia, L., +, TMTT July 2012 2287-2300 On the Detection of Frequency-Spectra-Based Chipless RFID Using UWB Impulsed Interrogation. Kalansuriya, P., +, TMTT Dec. 2012 4187-4197 Transparency Polarization-Independent Metamaterial Analog of Electromagnetically Induced Transparency for a Refractive-Index-Based Sensor. Meng, F.-Y., +, TMTT Oct. 2012 3013-3022 Traveling wave tubes Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes. Rouvalis, E., +, TMTT March 2012 509-517 Millimeter-Wave Optoelectronic Mixers Based on Uni-Traveling Carrier Photodiodes. Rouvalis, E., +, TMTT March 2012 686-691 Tuning A -Band Fully Tunable Cavity Filter. Yassini, B., +, TMTT Dec. 2012 4002-4012 A 64–84-GHz PLL With Low Phase Noise in an 80-GHz SiGe HBT Technology. Liu, G., +, TMTT Dec. 2012 3739-3748 Harmonic Suppressed Dual-Band Bandpass Filters With Tunable Passbands. Chaudhary, G., +, TMTT July 2012 2115-2123 Multilayer Antenna-Filter Antenna for Beam-Steering Transmit-Array Applications. Boccia, L., +, TMTT July 2012 2287-2300 Widely Tunable High-Efficiency Power Amplifier With Ultra-Narrow Instantaneous Bandwidth. Chen, K., +, TMTT Dec. 2012 3787-3797 Tunnel diodes Resonant Tunneling Diode Optoelectronic Circuits Applications in RadioOver-Fiber Networks. Cantu, H. I., +, TMTT Sept. 2012 2903-2912

U UHF amplifiers 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 A Wideband Low-Power CMOS LNA With Positive–Negative Feedback for Noise, Gain, and Linearity Optimization. Woo, S., +, TMTT Oct. 2012 3169-3178 Investigation of Wideband Load Transformation Networks for Class-E Switching-Mode Power Amplifiers. Wei, M.-D., +, TMTT June 2012 1916-1927 Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828 The Continuous Inverse Class-F Mode With Resistive Second-Harmonic Impedance. Carrubba, V., +, TMTT June 2012 1928-1936 Wideband CMOS Amplification Stage for a Direct-Sampling Square Kilometre Array Receiver. Navaratne, D., +, TMTT Oct. 2012 3179-3188 Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078 UHF antennas A Compact 3-D Harmonic Repeater for Passive Wireless Sensing. Nassar, I. T., +, TMTT Oct. 2012 3309-3316 Low-Power Wireless Power Delivery. Falkenstein, E., +, TMTT July 2012 2277-2286 UHF circuits Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology. Qian, S., +, TMTT Sept. 2012 2799-2807 UHF couplers 180 and 90 Reflection-Type Phase Shifters Using Over-Coupled Lange Couplers. Fang, H. R., +, TMTT Nov. 2012 3440-3448 A Directivity-Enhanced Directional Coupler Using Epsilon Negative Transmission Line. Pourzadi, A., +, TMTT Nov. 2012 3395-3402 A Dual-Band Coupled-Line Coupler With an Arbitrary Coupling Coefficient. Wang, X., +, TMTT April 2012 945-951 A Novel Dual-Band 3-dB Branch-Line Coupler Design With Controllable Bandwidths. Cheng, K.-K. M., +, TMTT Oct. 2012 3055-3061

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

UHF devices A Digital-Intensive Multimode Multiband Receiver Using a Sinc FilterEmbedded VCO-Based ADC. Kim, J., +, TMTT Oct. 2012 3254-3262 UHF diodes A Tunable Combline Bandpass Filter Loaded With Series Resonator. Wang, X.-G., +, TMTT June 2012 1569-1576 Low-Power Wireless Power Delivery. Falkenstein, E., +, TMTT July 2012 2277-2286 UHF filters A Quasi Elliptic Function 1.75–2.25 GHz 3-Pole Bandpass Filter With Bandwidth Control. Chiou, Y.-C., +, TMTT Feb. 2012 244-249 A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 A Tunable Combline Bandpass Filter Loaded With Series Resonator. Wang, X.-G., +, TMTT June 2012 1569-1576 Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators. Ahn, H.-R., +, TMTT June 2012 1549-1559 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Harmonic Suppressed Dual-Band Bandpass Filters With Tunable Passbands. Chaudhary, G., +, TMTT July 2012 2115-2123 Miniature Quasi-Lumped-Element Wideband Bandpass Filter at 0.5–2-GHz Band Using Multilayer Liquid Crystal Polymer Technology. Qian, S., +, TMTT Sept. 2012 2799-2807 UHF integrated circuits A Novel Carrier Leakage Suppression Front-End for UHF RFID Reader. Jung, J.-Y., +, TMTT May 2012 1468-1477 Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier. Saad, P., +, TMTT June 2012 1840-1849 Investigation of Wideband Load Transformation Networks for Class-E Switching-Mode Power Amplifiers. Wei, M.-D., +, TMTT June 2012 1916-1927 Wideband CMOS Amplification Stage for a Direct-Sampling Square Kilometre Array Receiver. Navaratne, D., +, TMTT Oct. 2012 3179-3188 UHF mixers A Low-Voltage, Low-Power, and Low-Noise UWB Mixer Using Bulk-Injection and Switched Biasing Techniques. Kim, M.-G., +, TMTT Aug. 2012 2486-2493 UHF oscillators A 50-Mb/s CMOS QPSK/O-QPSK Transmitter Employing Injection Locking for Direct Modulation. Diao, S., +, TMTT Jan. 2012 120-130 A Digital-Intensive Multimode Multiband Receiver Using a Sinc FilterEmbedded VCO-Based ADC. Kim, J., +, TMTT Oct. 2012 3254-3262 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Pulse-Biased Low-Power Low-Phase-Noise UHF LC-QVCO for 866 MHz RFID Front-End. Li, J., +, TMTT Oct. 2012 3120-3125 UHF phase shifters 180 and 90 Reflection-Type Phase Shifters Using Over-Coupled Lange Couplers. Fang, H. R., +, TMTT Nov. 2012 3440-3448 2–6-GHz BiCMOS Polar-Based Vector Modulator for - and -Band Diversity Receivers. Mayer, U., +, TMTT March 2012 567-573 A Full 360 Vector-Sum Phase Shifter With Very Low RMS Phase Error Over a Wide Bandwidth. Asoodeh, A., +, TMTT June 2012 1626-1634 UHF power amplifiers A 30.8-dBm Wideband CMOS Power Amplifier With Minimized Supply Fluctuation. Jin, B., +, TMTT June 2012 1658-1666 A 5-Gb/s 2.1–2.2-GHz Bandpass Modulator for Switch-Mode Power Amplifier. Ostrovskyy, P., +, TMTT Aug. 2012 2524-2531 A Fully Integrated Watt-Level Linear 900-MHz CMOS RF Power Amplifier for LTE-Applications. Francois, B., +, TMTT June 2012 1878-1885 A Simplified Broadband Design Methodology for Linearized High-Efficiency Continuous Class-F Power Amplifiers. Tuffy, N., +, TMTT June 2012 1952-1963 A Transformer-Less Load-Modulated (TLLM) Architecture for Efficient Wideband Power Amplifiers. Akbarpour, M., +, TMTT Sept. 2012 2863-2874 Analysis and Design of a Stacked Power Amplifier With Very High Bandwidth. Fritsche, D., +, TMTT Oct. 2012 3223-3231

+ Check author entry for coauthors

4291

Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 LDMOS Technology for RF Power Amplifiers. Theeuwen, S. J. C. H., +, TMTT June 2012 1755-1763 Mitigation of Bandwidth Limitation in Wireless Doherty Amplifiers With Substantial Bandwidth Enhancement Using Digital Techniques. Darraji, R., +, TMTT Sept. 2012 2875-2885 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 Peak-Power Controlled Digital Predistorters for RF Power Amplifiers. Landin, P. N., +, TMTT Nov. 2012 3582-3590 UHF resonators A Three-Pole 1.2–2.6-GHz RF MEMS Tunable Notch Filter With 40-dB Rejection and Bandwidth Control. Cheng, C.-C., +, TMTT Aug. 2012 24312438 UHF transistors A Low-Voltage, Low-Power, and Low-Noise UWB Mixer Using Bulk-Injection and Switched Biasing Techniques. Kim, M.-G., +, TMTT Aug. 2012 2486-2493 Ultra wideband communication Miniaturized UWB Filters Integrated With Tunable Notch Filters Using a Silicon-Based Integrated Passive Device Technology. Wu, Z., +, TMTT March 2012 518-527 Performance Enhancement of an OFDM Ultra-Wideband Transmission-Over-Fiber Link Using a Linearized Mixed-Polarization Single-Drive X-Cut Mach–Zehnder Modulator. Hraimel, B., +, TMTT Oct. 2012 3328-3338 Ultra-Wideband Single and Dual Baluns Based on Substrate Integrated Coaxial Line Technology. Zhu, F., +, TMTT Oct. 2012 3062-3070 Ultra wideband radar A -Band CMOS UWB Radar Transmitter With a Bi-Phase Modulating Pulsed Oscillator. Lee, S., +, TMTT May 2012 1405-1412 A 24-GHz CMOS UWB Radar Transmitter With Compressed Pulses. Yang, J., +, TMTT April 2012 1117-1125 A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading. Koswatta, R. V., +, TMTT Sept. 2012 2925-2933 An Ultra-Wideband 80 GHz FMCW Radar System Using a SiGe Bipolar Transceiver Chip Stabilized by a Fractional-N PLL Synthesizer. Pohl, N., +, TMTT March 2012 757-765 Buried Object Characterization Using Ultra-Wideband Ground Penetrating Radar. Li, L., +, TMTT Aug. 2012 2654-2664 Design and Analysis of a 21–29-GHz Ultra-Wideband Receiver Front-End in 0.18- m CMOS Technology. Lin, Y.-S., +, TMTT Aug. 2012 2590-2604 Passive Wireless Temperature Sensor Based on Time-Coded UWB Chipless RFID Tags. Girbau, D., +, TMTT Nov. 2012 3623-3632 Ultra wideband technology Design and Analysis of an Ultra-Wideband Automatic Self-Calibrating Upconverter in 65-nm CMOS. Kang, B., +, TMTT July 2012 2178-2191 Design Method for Ultra-Wideband Bandpass Filter With Wide Stopband Using Parallel-Coupled Microstrip Lines. Abbosh, A. M., +, TMTT Jan. 2012 31-38 Design of Transmission-Type th-Order Differentiators in Planar Microwave Technology. Chudzik, M., +, TMTT Nov. 2012 3384-3394 Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation. Jooyaie, A., +, TMTT Aug. 2012 2505-2511 Uncertainty A Unified Theory for -Parameter Uncertainty Evaluation. Garelli, M., +, TMTT Dec. 2012 3844-3855 Expedient Electromagnetic Analysis of the Impact of Statistical Disorder in Periodic Waveguides. Ochoa, J. S., +, TMTT Dec. 2012 3919-3926

V Vacuum breakdown Prediction of Multipactor Breakdown for Multicarrier Applications: The Quasi-Stationary Method. Anza, S., +, TMTT July 2012 2093-2105

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Varactors A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 A Highly Reconfigurable Low-Power CMOS Directional Coupler. Sun, J., +, TMTT Sept. 2012 2815-2822 A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 A Tunable Combline Bandpass Filter Loaded With Series Resonator. Wang, X.-G., +, TMTT June 2012 1569-1576 Broadband CMOS Millimeter-Wave Frequency Multiplier With Vivaldi Antenna in 3-D Chip-Scale Packaging. Tripodi, L., +, TMTT Dec. 2012 37613768 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology. Kuylenstierna, D., +, TMTT Nov. 2012 3420-3430 Digital Predistortion for High Efficiency Power Amplifier Architectures Using a Dual-Input Modeling Approach. Cao, H., +, TMTT Feb. 2012 361-369 Intrinsically Switched Varactor-Tuned Filters and Filter Banks. Guyette, A. C., +, TMTT April 2012 1044-1056 Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Low-Power Sub-Harmonic Direct-Conversion Receiver With Tunable RF LNA and Wideband LO Generator at U-NII Bands. Syu, J.-S., +, TMTT March 2012 555-566 Multilayer Antenna-Filter Antenna for Beam-Steering Transmit-Array Applications. Boccia, L., +, TMTT July 2012 2287-2300 On the Compression and Blocking Distortion of Semiconductor-Based Varactors. Huang, C., +, TMTT Dec. 2012 3699-3709 Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control. Serrano, A. L. C., +, TMTT March 2012 484-493 Theory and Design of Class-J Power Amplifiers With Dynamic Load Modulation. Andersson, C. M., +, TMTT Dec. 2012 3778-3786 Variable Reflection-Type Attenuators Based on Varactor Diodes. Bulja, S., +, TMTT Dec. 2012 3719-3727 Vectors Macromodeling of Distributed Networks From Frequency-Domain Data Using the Loewner Matrix Approach. Kabir, M., +, TMTT Dec. 2012 3927-3938 VLSI ParAFEMCap: A Parallel Adaptive Finite-Element Method for 3-D VLSI Interconnect Capacitance Extraction. Chen, G., +, TMTT Feb. 2012 218-231 Voltage control GaN HEMT Class E Resonant Topologies for UHF DC/DC Power Conversion. Garcia, J. A., +, TMTT Dec. 2012 4220-4229 Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. Jiang, T., +, TMTT Jan. 2012 170-178 Voltage measurement Controlling Active Load–Pull in a Dual-Input Inverse Load Modulated Doherty Architecture. Hone, T. M., +, TMTT June 2012 1797-1804 Voltage-controlled oscillators -Band CMOS Differential and Quadrature Voltage-Controlled Oscillators for Low Phase-Noise and Low-Power Applications. Chang, H.-Y., +, TMTT Jan. 2012 46-59 245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology. Mao, Y., +, TMTT Dec. 2012 3823-3833 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 A -Band Capacitor-Coupled QVCO Using Sinusoidal Current Bias Technique. Shen, I.-S., +, TMTT Feb. 2012 318-328 A 1.1-V Regulator-Stabilized 21.4-GHz VCO and a 115% Frequency-Range Dynamic Divider for -Band Wireless Communication. Nakamura, T., +, TMTT Sept. 2012 2823-2832 A 160-GHz Subharmonic Transmitter and Receiver Chipset in an SiGe HBT Technology. Zhao, Y., +, TMTT Oct. 2012 3286-3299 A 64–84-GHz PLL With Low Phase Noise in an 80-GHz SiGe HBT Technology. Liu, G., +, TMTT Dec. 2012 3739-3748 + Check author entry for coauthors

A Digital-Intensive Multimode Multiband Receiver Using a Sinc FilterEmbedded VCO-Based ADC. Kim, J., +, TMTT Oct. 2012 3254-3262 A Dual-Resonant Mode 10/22-GHz VCO With a Novel Inductive Switching Approach. Liu, S.-L., +, TMTT July 2012 2165-2177 A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 A Novel Reader Architecture Based on UWB Chirp Signal Interrogation for Multiresonator-Based Chipless RFID Tag Reading. Koswatta, R. V., +, TMTT Sept. 2012 2925-2933 A Self-Sustained Microwave System for Dielectric-Constant Measurement of Lossy Organic Liquids. Sekar, V., +, TMTT May 2012 1444-1455 A Sub-10 nJ/b 1.9-dBm Output Power FSK Transmitter for Body Area Network Applications. Masuch, J., +, TMTT May 2012 1413-1423 An Open-Loop Half-Quadrature Hybrid for Multiphase Signals Generation. Chen, H.-S., +, TMTT Jan. 2012 131-138 An RCP Packaged Transceiver Chipset for Automotive LRR and SRR Systems in SiGe BiCMOS Technology. Trotta, S., +, TMTT March 2012 778-794 Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters. Tseng, C.-H., +, TMTT Oct. 2012 3151-3160 Design of Low Phase-Noise Oscillators and Wideband VCOs in InGaP HBT Technology. Kuylenstierna, D., +, TMTT Nov. 2012 3420-3430 Experimental Characterization of Oscillator Circuits for Reduced-Order Models. Umpierrez, P., +, TMTT Nov. 2012 3527-3541 Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165 Low-Power-Consumption Wide-Locking-Range Dual-Injection-Locked 1/2 Divider Through Simultaneous Optimization of VCO Loaded and Current. Lee, S., +, TMTT Oct. 2012 3161-3168 Orthogonal -Wall and -Wall Tuning of Distributed Resonators: Using Concurrency for Continuous Ultra-Wideband Frequency Generation. Jooyaie, A., +, TMTT Aug. 2012 2505-2511 Pulse-Biased Low-Power Low-Phase-Noise UHF LC-QVCO for 866 MHz RFID Front-End. Li, J., +, TMTT Oct. 2012 3120-3125 Volterra series An Ultra-Low-Voltage and Low-Power 2 Subharmonic Downconverter Mixer. He, S., +, TMTT Feb. 2012 311-317 Modified Least Squares Extraction for Volterra-Series Digital Predistorter in the Presence of Feedback Measurement Errors. Liu, Y.-J., +, TMTT Nov. 2012 3559-3570 Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828

W

Wafer level packaging LDMOS Technology for RF Power Amplifiers. Theeuwen, S. J. C. H., +, TMTT June 2012 1755-1763 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Wave equations Characterization of Waveguides With a Combination of Conductor and Periodic Boundary Contours: Application to the Analysis of Bi-Periodic Structures. Varela, J. E., +, TMTT March 2012 419-430 Waveform analysis Parallel Frequency-Domain Simulation of Hyperspectral Waveforms in Nonlinear Power Amplifiers With Memory. Stantchev, G., +, TMTT April 2012 930-937 Waveguide antenna arrays A Small Package With 46-dB Isolation Between Tx and Rx Antennas Suitable for 60-GHz WPAN Module. Suga, R., +, TMTT March 2012 640-646 Waveguide components Low-Cost 60-GHz Smart Antenna Receiver Subsystem Based on Substrate Integrated Waveguide Technology. He, F. F., +, TMTT April 2012 11561165

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

Waveguide couplers A Dual-Band Coupled-Line Coupler With an Arbitrary Coupling Coefficient. Wang, X., +, TMTT April 2012 945-951 A High Slow-Wave Factor Microstrip Structure With Simple Design Formulas and Its Application to Microwave Circuit Design. Chang, W.-S., +, TMTT Nov. 2012 3376-3383 Authors’ reply. Lin, F., +, TMTT Sept. 2012 2935-2936 Comments on "Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter". Sun, Z., +, TMTT Sept. 2012 2934 Compact Tunable Reflection Phase Shifters Using Short Section of Coupled Lines. Abbosh, A. M., +, TMTT Aug. 2012 2465-2472 Quasi-Arbitrary Phase-Difference Hybrid Coupler. Wong, Y. S., +, TMTT June 2012 1530-1539 Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay. Zhang, Q., +, TMTT Aug. 2012 2394-2402 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Waveguide filters A Spurious-Free Discontinuous Galerkin Time-Domain Method for the Accurate Modeling of Microwave Filters. Alvarez, J., +, TMTT Aug. 2012 2359-2369 A Systematic Design Procedure of Classical Dual-Mode Circular Waveguide Filters Using an Equivalent Distributed Model. Cogollos, S., +, TMTT April 2012 1006-1017 A Temperature-Compensation Technique for Substrate Integrated Waveguide Cavities and Filters. Djerafi, T., +, TMTT Aug. 2012 2448-2455 Substrate Integrated Waveguide Quasi-Elliptic Filters With Controllable Electric and Magnetic Mixed Coupling. Gong, K., +, TMTT Oct. 2012 3071-3078 WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology. Leong, K. M. K. H., +, TMTT April 2012 9981005 Waveguide junctions A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the Turnstile Waveguide Circulator. Helszajn, J., +, TMTT Oct. 2012 3079-3087 Waveguide theory Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs. Rodriguez-Berral, R., +, TMTT March 2012 405-418 Waveguide transitions Vertical RF Transition With Mechanical Fit for 3-D Heterogeneous Integration. Chen, L., +, TMTT March 2012 647-654 Waveguides A Novel Compact Printable Dual-Polarized Chipless RFID System. Islam, M. A., +, TMTT July 2012 2142-2151 Even- and Odd-Mode Analysis of Thick and Wide Transverse Slot in Waveguides Based on a Variational Method. Wenzhi, W., +, TMTT Nov. 2012 3349-3358 Finite-Element Eigenvalue Analysis of Propagating and Evanescent Modes in 3-D Periodic Structures Using Model-Order Reduction. Bostani, A., +, TMTT Sept. 2012 2677-2683 Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements. Hu, F.-G., +, TMTT July 2012 2046-2054 Simulation and Measurement of the -Parameters of Obstacles in Periodic Waveguides. Navarro-Tapia, M., +, TMTT April 2012 1146-1155 Wearable antennas Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 Wide band gap semiconductors 3–3.6-GHz Wideband GaN Doherty Power Amplifier Exploiting Output Compensation Stages. Rubio, J. M., +, TMTT Aug. 2012 2543-2548 A 3-D Table-Based Method for Non-Quasi-Static Microwave FET Devices Modeling. Long, Y., +, TMTT Oct. 2012 3088-3095 A Monolithic AlGaN/GaN HEMT VCO Using BST Thin-Film Varactor. Kong, C., +, TMTT Nov. 2012 3413-3419 A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 A Simplified Broadband Design Methodology for Linearized High-Efficiency Continuous Class-F Power Amplifiers. Tuffy, N., +, TMTT June 2012 1952-1963

+ Check author entry for coauthors

4293

AlGaN/GaN HEMT With Distributed Gate for Channel Temperature Reduction. Darwish, A. M., +, TMTT April 2012 1038-1043 Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters. Hoversten, J., +, TMTT June 2012 2010-2020 Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier. Saad, P., +, TMTT June 2012 1840-1849 Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 Design of Adaptive Highly Efficient GaN Power Amplifier for Octave-Bandwidth Application and Dynamic Load Modulation. Chen, K., +, TMTT June 2012 1829-1839 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828 Switching Behavior of Class-E Power Amplifier and Its Operation Above Maximum Frequency. Jee, S., +, TMTT Jan. 2012 89-98 Wideband Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers. Yu, C., +, TMTT Dec. 2012 4198-4208 Wideband Dual-Mode Microstrip Filter Using Short-Ended Resonator With Centrally Loaded Inductive Stub. Sun, S.-J., +, TMTT Dec. 2012 3667-3673 Wideband amplifiers 3–3.6-GHz Wideband GaN Doherty Power Amplifier Exploiting Output Compensation Stages. Rubio, J. M., +, TMTT Aug. 2012 2543-2548 A 30.8-dBm Wideband CMOS Power Amplifier With Minimized Supply Fluctuation. Jin, B., +, TMTT June 2012 1658-1666 A Review of GaN on SiC High Electron-Mobility Power Transistors and MMICs. Pengelly, R. S., +, TMTT June 2012 1764-1783 A Transformer-Less Load-Modulated (TLLM) Architecture for Efficient Wideband Power Amplifiers. Akbarpour, M., +, TMTT Sept. 2012 2863-2874 A Wideband CMOS/GaAs HBT Envelope Tracking Power Amplifier for 4G LTE Mobile Terminal Applications. Hassan, M., +, TMTT May 2012 1321-1330 A Wideband Low-Power CMOS LNA With Positive–Negative Feedback for Noise, Gain, and Linearity Optimization. Woo, S., +, TMTT Oct. 2012 3169-3178 Broadband Doherty Power Amplifier via Real Frequency Technique. Sun, G., +, TMTT Jan. 2012 99-111 Compact Wideband Linear CMOS Variable Gain Amplifier for Analog-Predistortion Power Amplifiers. Huang, Y.-Y., +, TMTT Jan. 2012 68-76 Cryogenic Self-Calibrating Noise Parameter Measurement System. Russell, D., +, TMTT May 2012 1456-1467 Design of a Wideband High-Voltage High-Efficiency BiCMOS Envelope Amplifier for Micro-Base-Station RF Power Amplifiers. Kwak, M., +, TMTT June 2012 1850-1861 Investigation of Wideband Load Transformation Networks for Class-E Switching-Mode Power Amplifiers. Wei, M.-D., +, TMTT June 2012 1916-1927 Millimeter-Wave Self-Healing Power Amplifier With Adaptive Amplitude and Phase Linearization in 65-nm CMOS. Liu, J. Y.-C., +, TMTT May 2012 1342-1352 Multichannel and Wideband Power Amplifier Design Methodology for 4G Communication Systems Based on Hybrid Class-J Operation. Mimis, K., +, TMTT Aug. 2012 2562-2570 Multiharmonic Volterra Model Dedicated to the Design of Wideband and Highly Efficient GaN Power Amplifiers. Demenitroux, W., +, TMTT June 2012 1817-1828 Peak-Power Controlling Technique for Enhancing Digital Pre-Distortion of RF Power Amplifiers. Nader, C., +, TMTT Nov. 2012 3571-3581 Subsampling Feedback Loop Applicable to Concurrent Dual-Band Linearization Architecture. Bassam, S. A., +, TMTT June 2012 1990-1999 The Continuous Inverse Class-F Mode With Resistive Second-Harmonic Impedance. Carrubba, V., +, TMTT June 2012 1928-1936 Wideband Inductorless Balun-LNA Employing Feedback for Low-Power Low-Voltage Applications. Kim, J., +, TMTT Sept. 2012 2833-2842 Wideband LNA Using Active Inductor With Multiple Feed-Forward Noise Reduction Paths. Moezzi, M., +, TMTT April 2012 1069-1078

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WiMax A 30.8-dBm Wideband CMOS Power Amplifier With Minimized Supply Fluctuation. Jin, B., +, TMTT June 2012 1658-1666 Design of a Concurrent Dual-Band 1.8–2.4-GHz GaN-HEMT Doherty Power Amplifier. Saad, P., +, TMTT June 2012 1840-1849 Wire antennas A Fundamental Frequency 120-GHz SiGe BiCMOS Distance Sensor With Integrated Antenna. Sarkas, I., +, TMTT March 2012 795-812 Wireless channels Broadband Tissue-Equivalent Phantom for BAN Applications at Millimeter Waves. Chahat, N., +, TMTT July 2012 2259-2266 Wireless communication An Inkjet-Printed Solar-Powered Wireless Beacon on Paper for Identification and Wireless Power Transmission Applications. Kim, S., +, TMTT Dec. 2012 4178-4186 Wireless LAN 802.11a Compliant Spatial Diversity Receiver IC in 0.25- m BiCMOS. Wickert, M., +, TMTT April 2012 1097-1104 Broadband 57–64-GHz WLAN Communication System Integrated Into an Aircraft Cabin. Ziegler, V., +, TMTT Dec. 2012 4209-4219 Novel Modeling and Calibration Approach for Multiport Receivers Mitigating System Imperfections and Hardware Impairments. Hasan, A., +, TMTT Aug. 2012 2644-2653 Wireless sensor networks A Compact 3-D Harmonic Repeater for Passive Wireless Sensing. Nassar, I. T., +, TMTT Oct. 2012 3309-3316 Passive Wireless Temperature Sensor Based on Time-Coded UWB Chipless RFID Tags. Girbau, D., +, TMTT Nov. 2012 3623-3632 Wires A Comprehensive Analysis of the Absorption Spectrum of Conducting Ferromagnetic Wires. Liberal, I., +, TMTT July 2012 2055-2065

+ Check author entry for coauthors

A Physics-Based Causal Bond-Wire Model for RF Applications. Nazarian, A. L., +, TMTT Dec. 2012 3683-3692 Fe-Rich Ferromagnetic Wires for Mechanical-Stress Self-Sensing Materials. Liberal, I., +, TMTT Sept. 2012 2752-2759 Theory of Magnetic Transmission Lines. Brandao Faria, J. A., +, TMTT Oct. 2012 2941-2949 Woven composites Broadband Electromagnetic Modeling of Woven Fabric Composites. Mirotznik, M. S., +, TMTT Jan. 2012 158-169

Y

Yagi antenna arrays A 60-GHz Active Receiving Switched-Beam Antenna Array With Integrated Butler Matrix and GaAs Amplifiers. Patterson, C. E., +, TMTT Nov. 2012 3599-3607 Flip-Chip-Assembled -Band CMOS Chip Modules on Ceramic Integrated Passive Device With Transition Compensation for Millimeter-Wave System-in-Package Integration. Lu, H.-C., +, TMTT March 2012 766-777

Z

Zero voltage switching A Zero-Voltage-Switching Contour-Based Outphasing Power Amplifier. Singhal, N., +, TMTT June 2012 1896-1906

EDITORIAL BOARD Editor-in-Chief: GEORGE E. PONCHAK Associate Editors: H. ZIRATH, J.-S. RIEH, Q. XUE, L. ZHU, K. J. CHEN, M. YU, C.-W. TANG, N. S. BARKER, C. D. SARRIS, C. FUMEAUX, D. HEO, B. BAKKALOGLU, T.-S. HORNG, R. GOMEZ-GARCIA The following members reviewed papers during 2011

P. Aaen A. Abbaspour-Tamijani A. Abbosh D. Abbott A. Abdipour M. Abe M. Abegaonkar R. Abhari A. Abramowicz M. Acar L. Accatino R. Achar E. Ackerman J. Adam K. Agawa M. Ahmad H.-R. Ahn B. Ai M. Aikawa J. Aikio C. Aitchison M. Akaike T. Akin S. Aksoy I. Aksun A. Akyurtlu G. Ala L. Albasha A. Alexanian W. Ali-Ahmad F. Alimenti R. Allam K. Allen A. Alphones A. Alu A. Álvarez-Melcon A. Al-Zayed S. Amari H. Amasuga R. Amaya H. An D. Anagnostou M. Andersen K. Andersson M. Ando Y. Ando P. Andreani M. Andrés W. Andress K. Ang C. Angell I. Angelov Y. Antar G. Antonini H. Aoki V. Aparin F. Apollonio R. Araneo J. Archer F. Ares F. Ariaei T. Arima M. Armendariz L. Arnaut F. Arndt E. Artal H. Arthaber F. Aryanfar U. Arz M. Asai Y. Asano A. Asensio-Lopez K. Ashby H. Ashoka A. Atalar A. Atia S. Auster I. Awai A. Aydiner M. Ayza K. Azadet R. Azaro A. Babakhani P. Baccarelli M. Baginski I. Bahl S. Bajpai J. Baker-Jarvis B. Bakkaloglu M. Bakr A. Baladin C. Balanis S. Balasubramaniam J. Balbastre J. Ball P. Balsara Q. Balzano A. Banai S. Banba R. Bansal D. Barataud A. Barbosa F. Bardati I. Bardi J. Bardin A. Barel S. Barker F. Barnes J. Barr G. Bartolucci R. Bashirullan S. Bastioli A. Basu B. Bates R. Baxley Y. Bayram J.-B. Bégueret N. Behdad F. Belgacem H. Bell D. Belot J. Benedikt T. Berceli C. Berland M. Berroth G. Bertin E. Bertran A. Bessemoulin M. Beurden A. Bevilacqua A. Beyer M. Bialkowski

E. Biebl P. Bienstman S. Bila D. Blackham R. Blaikie M. Blank P. Blockley P. Blondy P. Blount D. Boccoli G. Boeck L. Boglione R. Boix G. Bonaguide F. Bonani G. Bonmassar O. Boos B. Borges V. Boria-Esbert O. Boric-Lubecke A. Borji S. Borm J. Bornemann W. Bosch R. Bosisio H. Boss G. Botta N. Boulejfen S. Boumaiza J. Bouny C. Boyd C. Bozler M. Bozzi R. Bradley D. Braess N. Braithwaite M. Brandolini G. Branner T. Brazil J. Breitbarth M. Bressan K. Breuer B. Bridges D. Bridges J. Brinkhoff E. Brown S. Brozovich E. Bryerton D. Budimir G. Burdge P. Burghignoli N. Buris C. C. Galup-Montoro B. Cabon P. Cabral L. Cabria C. Caloz C. Camacho-Peñalosa V. Camarchia E. Camargo R. Cameron M. Camiade C. Campbell M. Campovecchio F. Canavero A. Cangellaris A. Cantoni C. Cao F. Capolino F. Cappelluti G. Carchon J. Carmo K. Carr F. Carrez R. Carrillo-Ramirez P. Carro R. Carter N. Carvalho P. Casas R. Castello J. Catala M. Cavagnaro R. Caverly D. Cavigia J. Cazaux M. Celuch Z. Cendes D. Chadha M. Chae S. Chakraborty C. Chan C. Chang H. Chang K. Chang S. Chang T. Chang W. Chang E. Channabasappa H. Chapell W. Chappell C. Charles M. Chatras I. Chatterjee G. Chattopadhyay S. Chaudhuri S. Chebolu A. Cheldavi A. Chen C. Chen H. Chen J. Chen K. Chen M. Chen N. Chen S. Chen Y. Chen Z. Chen Z.-N. Chen H. Cheng K. Cheng M. Cheng Y. Cheng C. Cheon C. Chi M. Chia Y. Chiang J. Chiao A. Chin K. Chin H. Chiou Y. Chiou C. Chiu

H. Chiu A. Chizh C. Cho K. Cho T. Cho A. Choffrut C. Choi J. Choi W. Choi C. Chong M. Chongcheawchamnan C. Chou D. Choudhury E. Chow Y. Chow C. Christodoulou C. Christopoulos Q. Chu T. Chu H. Chuang M. Chuang Y. Chun S. Chung Y. Chung D. Chye A. Cidronali T. Cisco C. Cismaru O. Civi S. Clavijo M. Clénet D. Cogan P. Colantonio M. Cole J. Coleman J. Collantes R. Collin C. Collins B. Colpitts R. Compton G. Conciauro M. Condon D. Consonni A. Constanzo M. Converse K. Cools F. Cooray I. Corbella A. Costanzo S. Cotton C. Courtney G. Coutts J. Cowles J. Craninckx C. Crespo-Cadenas J. Cressler S. Cripps T. Crowe J. Cruz T. Cui E. Cullens T. Cunha W. Curtice J. Dabrowski W. Dai G. Dambrine P. Dankov F. Danneville I. Darwazeh A. Darwish N. Das M. Davidovich L. Davis D. Dawn J. Dawson H. Dayal F. De Flaviis D. De Zutter B. Deal A. Dearn J. Deen M. Dehan C. Dehollain C. Deibele G. Dejean M. DeLisio N. Deltimple S. Demir V. Demir J. Deng A. Dengi T. Denidni W. DeRaedt H. Deshpande Y. Deval R. Dey T. Dhaene L. Diaz A. Diaz-Morcillo L. Ding M. Dionigi C. Diskus A. Djordjevi T. Djordjevic J. Dobrowolski H. Dogan S. Donati X. Dong A. Dounavis P. Draxler R. Drayton A. Dreher J. Drewniak J. Duchamp A. Duffy L. Dunleavy J. Dunsmore S. Durden L. Dussopt C. Duvanaud J. East J. Ebel K. Eccleston I. Ederra R. Egri I. Ehrenberg N. Ehsan T. Eibert H. Eisele W. Eisenstadt G. Eleftheriades

F. Ellinger G. Ellis T. Ellis M. El-Nozahi M. Elsbury S. Elschner M. El-Shenawee T. Enoki K. Entesari L. Epp I. Erdin O. Ergul T. Eriksson C. Ernst D. Erricolo I. Eshrah M. Essaaidi H. Esteban C. Eswarappa W. Eyssa A. Ezzeddine C. Fager M. Fahmi Y. Fan D. Fang M. Farina A. Fathy M. Faulkner P. Fay A. Fazzi E. Fear P. Fedorenko D. Feld Y. Feng A. Feresidis A. Fernandez T. Fernandez M. Fernández-Barciela M. Ferndahl F. Fernez P. Ferrari E. Ferre-Pikal A. Ferrero M. Ferriss H. Fetterman J. Fiedziuszko S. Fiedziuszko G. Fikioris J. Fikioris I. Filanovsky F. Filicori D. Filipovic R. Fletcher B. Floyd H. Foltz N. Fong B. Fornberg F. Fortes K. Foster P. Foster P. Franzon A. Frappe J. Freire M. Freire A. Freundorfer F. Frezza I. Frigyes R. Frye J. Fu O. Fu R. Fujimoto O. Fujiwara C. Fumeaux C. Furse V. Fusco D. Gabbay E. Gad M. Gadringer N. Gagnon J. Gajadharsing A. Gala C. Galbraith B. Galwas J. Gambini A. Gameiro O. Gandhi B. Gao J. Gao S. Gao C. Gaquiere H. Garbe J. Garcia M. Garcia P. Garcia-Ducar F. Garcia-Vidal K. Gard P. Gardner P. Garland P. Gaudo J. Gautier S. Gedney B. Geelen F. Gekat B. Geller R. Genov A. Georgiadis N. Georgieva J. Gerdes W. Gerhard S. Gevorgian H. Ghali M. Ghanevati F. Ghannouchi K. Gharaibeh R. Gharpurey G. Ghione M. Ghovanloo F. Giannini A. Gibson I. Gil P. Gilabert B. Gimeno D. Ginste A. Goacher E. Godshalk A. Goel C. Goldsmith M. Golio M. Golosovsky R. Gómez-García A. Goncharenko X. Gong

R. Gonzalo S. Goodnick S. Gopalsami A. Gopinath A. Görür K. Gosalia M. Gouker K. Goverdhanam W. Grabherr J. Graffeuil L. Gragnani J. Grahn J. Grajal V. Granatstein A. Grbic A. Grebennikov I. Gresham A. Griol D. Grischowsky S. Grivet-Talocia E. Grossman S. Gruszczynski T. Grzegorczyk S. Guenneau T. Guerrero S. Gunnarsson J. Guo Y. Guo C. Gupta M. Gupta R. Gupta R. Gutmann W. Gwarek R. Habash S. Hadjiloucas D. Haemmerich M. Hagmann S. Hagness A. Halappa P. Hale D. Ham E. Hamidi O. Hammi H. Han T. Hancock A. Hanke G. Hanson Y. Hao Z. Hao R. Harjani L. Harle H. Harris P. Harrison O. Hartin J. Hasch H. Hashemi K. Hashimoto J. Haslett G. Hau S. Hauptmann L. Hayden L. He Y. He R. Heath E. Hegazi G. Hegazi S. Heinen W. Heinrich G. Heiter M. Hella R. Henderson F. Henkel B. Henning D. Heo K. Herrick F. Herzel J. Hesler J. Hesthaven K. Hettak H. Heuermann P. Heydari A. Hietala A. Higgins A. Hirata J. Hirokawa M. Ho K. Hoffmann R. Hoffmann E. Holzman V. Hombach J. Hong S. Hong W. Hong K. Honjo G. Hopkins Y. Horii J. Horng T.-S. Horng J. Horton K. Hosoya M. Hotta J. Hoversten J. Howard M. Høyerby H. Hsieh L. Hsieh C. Hsu H. Hsu J. Hsu C. Hsue R. Hu C. Huang F. Huang H. Huang P. Huang T. Huang J. Hubert W. Huei A. Hülsmann A. Hung C. Hung J. Hung I. Hunter I. Huynen H. Hwang J. Hwang K. Hwang R. Hwang G. Iannaccone K. Ikossi M. Isaksson T. Ishizaki

Digital Object Identifier 10.1109/TMTT.2012.2234367

S. Islam M. Ito K. Itoh T. Itoh Y. Itoh A. Ittipiboon F. Ivanek D. Iverson M. Iwamoto D. Jablonski D. Jachowski C. Jackson D. Jackson R. Jackson A. Jacob K. Jacobs S. Jacobsen D. Jaeger J. Jaeger S. Jagannathan N. Jain G. James M. Janezic S. Jang M. Jankovic D. Jansen L. Jansson H. Jantunen H. Jardon-Aguilar J. Jargon N. Jarosik B. Jarry P. Jarry A. Jastrzebski B. Jemison W. Jemison S. Jeng A. Jenkins S. Jeon D. Jeong J. Jeong Y. Jeong A. Jerng T. Jerse T. Jiang X. Jiang G. Jianjun D. Jiao J. Jin J. M. Jin J. Joe T. Johnson B. Jokanovic U. Jordan K. Joshin J. Joubert S. Jung T. Kaho S. Kanamaluru K. Kanaya S. Kang P. Kangaslahti B. Kapilevich I. Karanasiou M. Karim T. Kataoka A. Katz R. Kaul R. Kaunisto T. Kawai S. Kawasaki M. Kazimierczuk L. Kempel P. Kenington P. Kennedy A. Kerr D. Kettle A. Khalil W. Khalil S. Khang A. Khanifar A. Khanna R. Khazaka J. Khoja S. Kiaei J. Kiang B. Kim C. Kim D. Kim H. Kim I. Kim J. Kim S. Kim T. Kim W. Kim N. Kinayman R. King N. Kinzie S. Kirchoefer A. Kirilenko M. Kishihara T. Kitazawa J. Kitchen T. Klapwijk E. Klumperink D. Klymyshyn L. Knockaert R. Knoechel M. Koch K. Koh N. Kolias J. Komiak A. Komijani G. Kompa A. Konanur A. Konczykowska H. Kondoh B. Kopp B. Kormanyos J. Korvink P. Kosmas Y. Kotsuka S. Koziel A. Kozyrev V. Krishnamurthy H. Krishnaswamy C. Krowne J. Krupka D. Kryger H. Ku H. Kubo A. Kucar A. Kucharski

C. Kudsia A. Kudymov D. Kuester B. Kuhn W. Kuhn T. Kuki A. Kumar J. Kuno C. Kuo J.-T. Kuo H. Kurebayashi F. Kuroki L. Kushner S. Kusunoki D. Kuylenstierna Y. Kwon G. Kyriacou A. Lacaita J. Lamb P. Lampariello U. Langmann T. Larsen L. Larson J. Laskar C. Lau K. Lau A. Lauer D. Lautru P. Lavrador A. Lavrinenko A. Lazaro G. Lazzi R. Lech B. Lee C.-H. Lee C. Lee H. Lee J. Lee J.-H. Lee K. Lee R. Lee S. Lee T. Lee Y. Lee D. Leenaerts Z. Lei G. Leizerovich K. Leong Y. Leong R. Leoni C. Ler G. Leuzzi B. Levitas R. Levy C. Li L. Li M. Li X. Li L. Lianming C. Liao S. Liao D. Lie E. Lima E. Limiti F. Lin J. Lin K. Lin T. Lin Y. Lin S. Lindenmeier A. Lindner F. Ling D. Linkhart P. Linnér D. Linten D. Linton D. Lippens F. Little V. Litvinov C. Liu H. Liu J. Liu K. Liu Q. Liu S. Liu Y. Liu Z. Liu A. Llewandowski O. Llopis I. Lo L. Locht A. Loke K. Lonngren T. Lopetegi N. Lopez U. Lott G. Lovat D. Lovelace Z. Low C. Lu L. Lu S. Lu Y. Lu V. Lubecke S. Lucyszyn D. Ludwig N. Luhmann M. Lui J. Luy G. Lyons A. M. Niknejad K. Ma T.-G. Ma Z. Ma S. Maas P. Maccarini G. Macchiarella J. Machac B. Machiels M. Madihian A. Madjar G. Magerl S. Magierowski R. Mahmoudi I. Maio F. Maiwald A. Majedi H. Majedi M. Majewski M. Makimoto R. Makinen D. Malocha J. Manges

R. Mansour D. Manstretta J. Mao S. Mao F. Maradei A. Margomenos D. Markovic E. Márquez-Segura J. Martens F. Martin E. Martini K. Maruhashi J. Marzo D. Masotti A. Massa G. Massa F. Mastri J. Mateu A. Matsushima M. Mattes G. Matthaei K. Mayaram M. Mayer U. Mayer W. Mayer J. Mazeau S. Mazumder A. Mazzanti G. Mazzarella K. McCarthy G. McDonald I. McGregor M. McKinley J. McLean D. McQuiddy A. Mediano F. Medina M. Megahed I. Mehdi K. Mehrany A. Melcon R. Melville F. Mena D. Mencarelli C. Meng R. Menozzi W. Menzel P. Mercier B. Merkl F. Mesa R. Metaxas A. Metzger P. Meyer P. Mezzanotte E. Michielsen A. Mickelson D. Miller P. Millot J. Mingo F. Miranda D. Mirshekar A. Mirzaei S. Mitilineos R. Miyamoto K. Mizuno J. Modelski W. Moer M. Moghaddam A. Mohammadi S. Mohammadi A. Mohammadian P. Mohseni E. Moldovan M. Mollazadeh M. Mongiardo P. Monteiro J. Montejo-Garai G. Montoro J. Monzó-Cabrera J. Morente T. Morf D. Morgan M. Morgan A. Morini A. Morris J. Morsey A. Mortazawi M. Moussa M. Mrozowski Q. Mu J.-E. Mueller J. Muldavin K. Murata S.-S. Myoung M. Myslinski B. Nabet V. Nair K. Naishadham Y. Nakasha M. Nakatsugawa M. Nakhla J.-C. Nallatamby I. Nam S. Nam J. Nanzer T. Narhi A. Nashashibi A. Natarajan J. Nath A. Navarrini J. Navarro J. Nebus R. Negra J. Neilson B. Nelson P. Nepa A. Neri H. Newman G. Ng D. Ngo E. Ngoya C. Nguyen E. Nicol A. Nicolet S. Nicolson E. Niehenke M. Nielsen K. Nikita P. Nikitin N. Nikolova M. Nisenoff K. Nishikawa T. Nishino

G. Niu B. Noori C. Nordquist B. Notaros K. Noujeim D. Novak I. Novak G. Nusinovich K. O I. Obeid J. Obregon R. O’Dea M. O’Droma M. Odyniec J.-E. Oh T. Ohira E. Öjefors H. Okazaki V. Okhmatovski A. Oki M. Okumura G. Olbrich S. Olson F. Olyslager A. Omar K. Onodera B.-L. Ooi S. Ootaka H. Oraizi G. Orengo A. Orlandi R. Orta J. Ortega-Gonzalez S. Ortiz S. Otaka B. Otis K. Ozdemir T. Ozdemir O. Ozlem P. Paco R. Paknys S. Pal Y. Palaskas D. Palmer S. Pamarti G.-W. Pan S.-K. Pan A. Panariello K. Pance J. Papapolymerou S. Parisi C.-S. Park E. Park J.-S. Park M.-J. Park S. Park W. Park A. Parker T. Parker D. Pasquet M. Pastorino H. Pau S. Paulotto A. Pavio D. Pavlidis W. Pearson J.-C. Pedro S. Peik S. Pellerano G. Pelosi M. Pelosi D. Pelz R. Pengelly J. Pereda F. Pereira A. Perennec B. Perlman D. Peroulis L. Perregrini K. Per-Simon M. Persson M. Petelin A. Peterson A. Petosa O. Peverini U. Pfeiffer A.-V. Pham J. Phillips H. Pickett M. Pieraccini L. Pierantoni B. Pillans S. Pinel Z. Ping M. Pirola S. Pisa G. Pisano D. Pissoort D. Plant C. Plett J. Plumridge C. Pobanz A. Poddar F. Podevin R. Pogorzelski G. Ponchak A. Poon D. Popovic Z. Popovic J. Portilla M. Pospieszalski A. Pothier K. Pourvoyeur J. Powell H. Powen R. Prabhu L. Pradell S. Prasad D. Prather A. Priou S. Pruvost Y. Qian R. Qiang J. Qiu T. Quach X. Quan R. Quay C. Queck C. Quendo R. Quéré F. Quesada F. Raab V. Radisic

M. Raffetto A. Raffo T. Rahkonen R. Raich A. Raisanen O. Ramahi M. Ramdani R. Ranson P. Rantakari L. Ranzani P. Ratajczak H. Rategh C. Rauscher J. Rautio T. Rautio B. Rawat J. Rayas-Sanchez G. Rebeiz J. Rebollar M. Reddy J. Reid R. Reid J. Reina-Tosina S. Reising B. Rembold K. Remley R. Renaut S. Rengarajan D. Resca P. Reynaert S. Reynolds A. Rezazadeh E. Rezek S. Ricci A. Riddle L. Rienzo D. Ritter E. Rius J. Rizk V. Rizzoli M. Roberg I. Robertson P. Roblin A. Roden C. Rodenbeck W. Rodriguez F. Rodriguez-Morales M. Rodwell A. Rofougaran R. Rogers H. Rogier U. Rohde V. Rokhlin Y. Rolain J.-M. Rollin R. Romanofsky S. Romisch G. Romo Y. Rong D. Rönnow D. Root N. Rorsman M. Rosario L. Roselli A. Rosen U. Rosenberg M. Rosker T. Roste F. Rotella E. Rothwell R. Rotman P. Rovati J. Roy L. Roy M. Roy T. Rozzi T. Rubaek J. Rubio D. Rudolph M. Rudolph A. Ruehli C. Ruppel A. Rydberg J. Ryynänen C. Saavedra F. Sabath K. Sachse B. Sadler N. Safari A. Safarian A. Safavi-Naeini A. Safwat P. Saha K. Saito I. Sakagami S. Sakhnenko T. Samaras J. Sambles C. Samori A. Sanada J. Sanchez S. Sancho K. Sano A. Santarelli H. Santos S. Sanyal K. Sarabandi T. Sarkar C. Sarris H. Sato P. Saunier M. Sawan H. Sayadian A. Sayeed W. Scanlon E. Schamiloglu J. Schellenberg M. Schindler E. Schlecht E. Schmidhammer L.-P. Schmidt S. Schmidt D. Schmitt F.-J. Schmueckle J. Schoebel D. Schreurs D. Schrijver A. Schuchinsky P. Schuh L. Schulwitz K. Schünemann J. Schutt-Aine

J. Scott F. Sechi K. Sellal V. Semenov E. Semouchkina K.-S. Seo J. Sercu A. Serebryannikov J. Sevic O. Sevimli F. Seyfert L. Shafai A. Shameli O. Shanaa Z. Shao I. Shapir A. Sharma S. Sharma J. Sharp D. Sheen T. Shen Z. Shen Y. Shestopalov J. Shi Y.-Q. Shi H. Shigematsu Y. Shih H. Shin S. Shin S.-H. Shin N. Shino W. Shiroma S. Shitov K. Shu D. Shyroki D. Sievenpiper C. Silva D. Silveira M. Silveirinha K. Silvonen W. Simbuerger G. Simin R. Simons C. Simovsky J. Simpson V. Simulik D. Simunic H. Singh D. Sinnott Z. Sipus C. Siviero H. Sjöland M. Slazar-Palma R. Sloan P. Smith C. Snowden R. V. Snyder M. Sobhy A. Sodagar N. Sokal K. Solbach J. Sombrin Y.-K. Song R. Sorrentino A. Soury E. Sovero J. Sowers R. Sperlich B. Spielman K. Stadius P. Staecker D. Staiculescu D. Stancil A. Stancu A. Stanitzki S. Stapleton J. Staudinger P. Stauffer B. Stec D. Steenson P. Steenson M. Steer G. Stegmayer J. Stenarson B. Stengel K. Stephan C. Stevens N. Stevens M. Steyaert J. Stiens I. Stievano S. Stitzer M. Straayer B. Strassner A. Street W. Struble M. Stubbs M. Stuchly B. Stupfel A. Suárez G. Subramanyam T. Sudo N. Suematsu T. Suetsugu C. Sullivan F. Sullivan A. Sulyman N. Sun S. Sun X. Sun R. Sutton K. Suzuki J. Svacina M. Swaminathan D. Swanson B. Szendrenyi W. Tabbara A. Taflove Y. Tajima T. Takagi M. Takahashi I. Takenaka T. Takenaka V. Talanov S. Talisa K.-W. Tam B. Tan E. Tan J. Tan T. Tanaka C.-W. Tang W.-C. Tang

X.-H. Tang T. Taris R. Tascone P. Tasker J. Taub J. Tauritz V. Tavares S. Taylor D. Teeter R. Temkin M. Tentzeris V. Teppati J.-P. Teyssier N. Thakor H. Thal J. Tham M. Thumm M. Tiebout E. Tiiliharju M.-R. Tofighi P. Tognolatti T. Toifl T. Tokumitsu A. Tombak A. Topa E. Topsakal H. Torres-Silva G. Town S. Tretyakov R. Trew P. Troyk C. Trueman A. Truitt C.-M. Tsai Z.-M. Tsai J. Tsalamengas C.-H. Tseng T. Tsiboukis J. Tsui M. Tsutsumi S. H.-L. Tu W.-H. Tu N. Tufillaro V. Turin G. Twomey C.-K. Tzuang T. Ueda V. Urick K. U-Yen N. Uzunoglu T. Vähä-Heikkilä R. Vahldieck A. Valdovinos G. Vandenbosch K. Vanhille D. Vanhoenacker-Janvier G. Vannini L. Vardapetyan G. Vasilescu C. Vaucher J. Vaz L. Vegni G. Vendelin S. Verdeyme M. Vérez A. Verma J. Verspecht P. Vial H.-O. Vickes A. Victor L. Vietzorreck C. Vittoria S. Vitusevich R. Voelker S. Voinigescu J. Volakis A. Vorst M. Vossiek M. Vouvakis B. Vowinkel L. Vreede K. Vryssas C. Wagner B. Waldmann P. Waldow A. Walker P. Wambacq S. Wane B.-Z. Wang C. Wang C.-F. Wang C.-J. Wang E. Wang F. Wang H. Wang J. Wang K.-C. Wang N. Wang X. Wang Y. Wang Y.-H. Wang Z.-G. Wang C. Ward J. Ward W. Wattanapanitch J. Webb D. Webster R. Webster S. Wedge J. Weem X. Wei D. Weide R. Weigel R. Weikle C. Weil T. Weiland D. Weile S. Weinreb M. Weiss S. Weiss T. Weller C. Wen G. Wen S. Wentworth D. Wentzloff R. Wenzel J. Whelehan J. Whitaker J. White J. Wiart M. Wickert

A. Wiesbauer J. Wight D. Willems B. Willemsen D. Williams A. Williamson J. Wilson J. Wiltse T. Winkel K. Wise D. Wisell M. Wolf E. Wollack G. Wollenberg F. Wong K. Wong M. Wong S. Wong K. Woo J. Wood G. Woods D. Woolard C. Wu J.-M. Wu K.-L. Wu K. Wu L. Wu R.-B. Wu T. Wu T.-L. Wu R. Wylde T. Wysocki M. Xia S. Xiang J. Xiao Y. Xiao C. Xie J. Xu S. Xu Q. Xue M. Yagoub T. Yakabe A. Yakovlev K. Yamamoto K. Yamauchi W. Yan C.-L. Yang F. Yang N. Yang X. Yang Y. Yang Z. Yang F. Yanovsky H.-W. Yao J. Yao A. Yarovoy Y. Yashchyshyn K. Yashiro K. Yasumoto J. Yau S. Ye J. Yeh K.-S. Yeo S.-P. Yeo K.-W. Yeom L.-K. Yeung W.-Y. Yin X.-S. Yin S. Yngvesson D. Yongsheng D. Yoo H.-J. Yoo J.-G. Yook E. Yoon J.-B. Yoon R. York S. Yoshikado A. Young B. Young D. Young P. Young W. Young H.-K. Yu M. Yu P. Yu R. Yu W. Yu Y. Yu M. Yuan M. Yuce S.-W. Yun F. Zabini J. Zaeytijd K. Zaki P. Zampardi J. Zapata L. Zappelli C. Zelley P. Zhai C. Zhang F. Zhang G. Zhang H. Zhang J. Zhang N. Zhang Q.-J. Zhang R. Zhang Y. Zhang A.-P. Zhao Y.-J. Zhao Y. Zhao Y. Zheng Q. Zhiguo H. Zhou A. Zhu L. Zhu N.-H. Zhu X. Zhu J. Zhuang H. Zirath